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Jun 30, 2018
06/18

by
Gesualdo Delfino

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We consider the unitary time evolution of a one-dimensional quantum system which is in a stationary state for negative times and then undergoes a sudden change (quench) of a parameter of its Hamiltonian at t=0. For systems possessing a continuum limit described by a massive quantum field theory we investigate in general perturbative quenches for the case in which the theory is integrable before the quench.

Topics: High Energy Physics - Theory, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1405.6553

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Sep 19, 2013
09/13

by
Gesualdo Delfino

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The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and confinement. Here we discuss how Ising field theory also gives the simplest model for particle decay. The decay widths computed in this theory provide the obvious test ground for the numerical methods designed to study unstable particles in quantum field theories...

Source: http://arxiv.org/abs/hep-th/0703288v1

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Sep 23, 2013
09/13

by
Gesualdo Delfino

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We introduce the notion of parafermionic fields as the chiral fields which describe particle excitations in two-dimensional conformal field theory, and argue that the parafermionic conformal dimensions can be determined using scale invariant scattering theory. Together with operator product arguments this may provide new information, in particular for non-rational conformal theories. We obtain in this way the field theoretical derivation of the critical exponents of the random cluster and O(n)...

Source: http://arxiv.org/abs/1212.3178v2

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Sep 18, 2013
09/13

by
Gesualdo Delfino

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For a large class of integrable quantum field theories we show that the S-matrix determines a space of fields which decomposes into subspaces labeled, besides the charge and spin indices, by an integer k. For scalar fields k is non-negative and is naturally identified as an off-critical extension of the conformal level. To each particle we associate an operator acting in the space of fields whose eigenvectors are primary (k=0) fields of the massive theory. We discuss how the existing results...

Source: http://arxiv.org/abs/0806.1883v1

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Jun 26, 2018
06/18

by
Gesualdo Delfino

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We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical case, considering systems both on the whole plane and in presence of boundaries. The topics we discuss include magnetism, percolation, phase separation, interfaces, wetting.

Topics: Statistical Mechanics, High Energy Physics - Theory, Mathematics, Mathematical Physics, Condensed...

Source: http://arxiv.org/abs/1502.05538

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Jun 29, 2018
06/18

by
Gesualdo Delfino

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The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk correlation length critical exponent $\nu$ is larger than or equal to 1. Interaction with a boundary or defect line involves an additional scale and a dependence of the localization strength on the distance from criticality. The implications are particularly rich...

Topics: High Energy Physics - Theory, Statistical Mechanics, Condensed Matter, High Energy Physics - Lattice

Source: http://arxiv.org/abs/1601.01189

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Sep 23, 2013
09/13

by
Gesualdo Delfino

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The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties, exact results for the magnetic case have been missing until the late eighties, when A.Zamolodchikov solved the model in a field at the critical temperature, directly in the scaling limit, within the framework of integrable quantum field theory. In this article...

Source: http://arxiv.org/abs/hep-th/0312119v1

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Sep 21, 2013
09/13

by
Gesualdo Delfino

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The clusters of up spins of a two-dimensional Ising ferromagnet undergo a second order percolative transition at temperatures above the Curie point. We show that in the scaling limit the percolation threshold is described by an integrable field theory and identify the non-perturbative mechanism which allows the percolative transition in absence of thermodynamic singularities. The analysis is extended to the Kertesz line along which the Coniglio-Klein droplets percolate in a positive magnetic...

Source: http://arxiv.org/abs/0902.3339v1

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Jun 30, 2018
06/18

by
Gesualdo Delfino

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We consider the broken phase of the n-vector model in n+1 dimensions with boundary conditions enforcing the presence of topological defect lines (Ising domain walls, XY vortex lines, and so on), and use field theory to argue an exact expression for the order parameter.

Topics: High Energy Physics - Theory, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1401.2041

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Sep 18, 2013
09/13

by
Gesualdo Delfino

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We use the results of integrable field theory to determine the universal amplitude ratios in the two-dimensional Ising model. In particular, the exact values of the ratios involving amplitudes computed at nonzero magnetic field are provided.

Source: http://arxiv.org/abs/hep-th/9710019v2

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Sep 18, 2013
09/13

by
Gesualdo Delfino

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In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behaviour in antiferromagnetic systems. It is an interesting question to investigate how the memory of the lattice survives in the field theory describing a scaling antiferromagnet. We discuss this issue for the square lattice three-state Potts model, whose scaling limit as T->0 is argued to be described exactly by the sine-Gordon field theory at a...

Source: http://arxiv.org/abs/hep-th/0110181v1

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Jun 30, 2018
06/18

by
Gesualdo Delfino; Alessio Squarcini

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The exact theory of phase separation in a two-dimensional wedge is derived from the properties of the order parameter and boundary condition changing operators in field theory. For a shallow wedge we determine the passage probability for an interface with endpoints on the boundary. For generic opening angles we exhibit the fundamental origin of the filling transition condition and of the property known as wedge covariance.

Topics: High Energy Physics - Theory, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1403.1138

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Jun 28, 2018
06/18

by
Gesualdo Delfino; Alessio Squarcini

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We consider a statistical system in a planar wedge, for values of the bulk parameters corresponding to a first order phase transition and with boundary conditions inducing phase separation. Our previous exact field theoretical solution for the case of a single interface is extended to a class of systems, including the Blume-Capel model as the simplest representative, allowing for the appearance of an intermediate layer of a third phase. We show that the interfaces separating the different...

Topics: Mathematical Physics, Statistical Mechanics, Mathematics, Condensed Matter, High Energy Physics -...

Source: http://arxiv.org/abs/1509.00310

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Sep 21, 2013
09/13

by
Gesualdo Delfino; Giuliano Niccoli

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Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model.

Source: http://arxiv.org/abs/hep-th/0407142v2

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4.0

Jun 29, 2018
06/18

by
Gesualdo Delfino; Jacopo Viti

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The theory of quantum quenches in near-critical one-dimensional systems formulated in [J. Phys. A 47 (2014) 402001] yields analytic predictions for the dynamics, unveils a qualitative difference between non-interacting and interacting systems, with undamped oscillations of one-point functions occurring only in the latter case, and explains the presence and role of different time scales. Here we examine additional aspects, determining in particular the relaxation value of one-point functions for...

Topics: High Energy Physics - Theory, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1608.07612

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Sep 23, 2013
09/13

by
Gesualdo Delfino; Jacopo Viti

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We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of sides much larger than the correlation length and for the mean number of such crossing clusters.

Source: http://arxiv.org/abs/1110.6355v2

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Sep 22, 2013
09/13

by
Gesualdo Delfino; Giuliano Niccoli

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The form factors of the descendant operators in the massive Lee-Yang model are determined up to level 7. This is first done by exploiting the conserved quantities of the integrable theory to generate the solutions for the descendants starting from the lowest non-trivial solutions in each operator family. We then show that the operator space generated in this way, which is isomorphic to the conformal one, coincides, level by level, with that implied by the $S$-matrix through the form factor...

Source: http://arxiv.org/abs/hep-th/0501173v1

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46

Sep 19, 2013
09/13

by
Gesualdo Delfino; Jacopo Viti

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We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.

Source: http://arxiv.org/abs/1009.1314v1

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Jun 29, 2018
06/18

by
Gesualdo Delfino; Alessio Squarcini

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We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation generates long range correlations in the direction parallel to the interface, and determine their exact analytic form. The latter leads to specific contributions to the structure factor of the interface.

Topics: High Energy Physics - Theory, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1607.01275

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Sep 21, 2013
09/13

by
Gesualdo Delfino; Paolo Grinza

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The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q=4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for both mesons and baryons. Deconfined quarks (kinks) exist in a phase bounded by a first order transition...

Source: http://arxiv.org/abs/0706.1020v2

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Sep 21, 2013
09/13

by
Gesualdo Delfino; Jacopo Viti

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We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that of independent n-point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the...

Source: http://arxiv.org/abs/1104.4323v2

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4.0

Jun 30, 2018
06/18

by
Gesualdo Delfino; Alessio Squarcini

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We consider the decay of the thermodynamic Casimir force in phases with a finite correlation length. For the case of the strip, we use properties of low energy two-dimensional field theory to show that the decay depends on the symmetry properties of the boundary conditions, in distinctive ways that we determine exactly. Features characteristic of the bulk universality class may induce modifications that we also discuss. Symmetry breaking and symmetry preserving boundary conditions exchange...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1410.3283

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46

Sep 21, 2013
09/13

by
Gesualdo Delfino; Giuliano Niccoli

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The composite operator T\bar{T}, obtained from the components of the energy-momentum tensor, enjoys a quite general characterization in two-dimensional quantum field theory also away from criticality. We use the form factor bootstrap supplemented by asymptotic conditions to determine its matrix elements in the sinh-Gordon model. The results extend to the breather sector of the sine-Gordon model and to the minimal models M_{2/(2N+3)} perturbed by the operator phi_{1,3}.

Source: http://arxiv.org/abs/hep-th/0602223v1

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46

Sep 23, 2013
09/13

by
Gesualdo Delfino; Jacopo Viti

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Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use integrable field theory to determine amplitude ratios which characterize the approach to criticality within these two universality classes of percolative critical behavior.

Source: http://arxiv.org/abs/1006.2301v1

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Sep 23, 2013
09/13

by
Gesualdo Delfino; Alessio Squarcini

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We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties of low energy two-dimensional field theory to determine exact asymptotics of the magnetization profile perperdicularly to the boundary, to show the presence of an interface with endpoints pinned to the boundary, and to determine its passage probability. The...

Source: http://arxiv.org/abs/1303.1938v1

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Sep 22, 2013
09/13

by
Gesualdo Delfino; Jacopo Viti; John Cardy

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We complete the determination of the universal amplitude ratios of two-dimensional percolation within the two-kink approximation of the form factor approach. For the cluster size ratio, which has for a long time been elusive both theoretically and numerically, we obtain the value 160.2, in good agreement with the lattice estimate 162.5 +/- 2 of Jensen and Ziff.

Source: http://arxiv.org/abs/1001.5424v1

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Sep 19, 2013
09/13

by
Luca Lepori; Gabor Zsolt Toth; Gesualdo Delfino

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The three-state Potts field theory in two dimensions with thermal and magnetic perturbations provides the simplest model of confinement allowing for both mesons and baryons, as well as for an extended phase with deconfined quarks. We study numerically the evolution of the mass spectrum of this model over its whole parameter range, obtaining a pattern of confinement, particle decay and phase transitions which confirms recent predictions.

Source: http://arxiv.org/abs/0909.2192v2