63 research outputs found
Field theory of Ising percolating clusters
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 field.Comment: 19 pages, 8 figure
Matrix elements of the operator T\bar{T} in integrable quantum field theory
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.Comment: 22 pages, one reference adde
The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
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}.Comment: 29 page
Phase separation and interface structure in two dimensions from field theory
We study phase separation in two dimensions in the scaling limit below
criticality. The general form of the magnetization profile as the volume goes
to infinity is determined exactly within the field theoretical framework which
explicitly takes into account the topological nature of the elementary
excitations. The result known for the Ising model from its lattice solution is
recovered as a particular case. In the asymptotic infrared limit the interface
behaves as a simple curve characterized by a gaussian passage probability
density. The leading deviation, due to branching, from this behavior is also
derived and its coefficient is determined for the Potts model. As a byproduct,
for random percolation we obtain the asymptotic density profile of a spanning
cluster conditioned to touch only the left half of the boundary.Comment: 12 pages, 3 figures; published version, references adde
Universal amplitude ratios in the two-dimensional Ising model
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.Comment: 9 pages; a factor 8/15 included in the amplitude A_c and the ratio
R_A, typos correcte
Correlation spreading and properties of the quantum state in quench dynamics
The light cone spreading of correlations following a quantum quench is obtained from first principles. Fully taking into account quantum and interaction effects, the derivation shows how light cone dynamics does not require peculiar properties of the postquench state
Field theory of Ising percolating clusters
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 field.Comment: 19 pages, 8 figure
Particles, conformal invariance and criticality in pure and disordered systems
The two-dimensional case occupies a special position in the theory of
critical phenomena due to the exact results provided by lattice solutions and,
directly in the continuum, by the infinite-dimensional character of the
conformal algebra. However, some sectors of the theory, and most notably
criticality in systems with quenched disorder and short range interactions,
have appeared out of reach of exact methods and lacked the insight coming from
analytical solutions. In this article we review recent progress achieved
implementing conformal invariance within the particle description of field
theory. The formalism yields exact unitarity equations whose solutions classify
critical points with a given symmetry. It provides new insight in the case of
pure systems, as well as the first exact access to criticality in presence of
short range quenched disorder. Analytical mechanisms emerge that in the random
case allow the superuniversality of some critical exponents and make explicit
the softening of first order transitions by disorder.Comment: Invited Colloquium articl
Space of initial conditions and universality in nonequilibrium quantum dynamics
We study analytically the role of initial conditions in nonequilibrium
quantum dynamics considering the one-dimensional ferromagnets in the regime of
spontaneously broken symmetry. We analyze the expectation value of local
operators for the infinite-dimensional space of initial conditions of domain
wall type, generally intended as initial conditions spatially interpolating
between two different ground states. At large times the unitary time evolution
takes place inside a light cone produced by the spatial inhomogeneity of the
initial condition. In the innermost part of the light cone the form of the
space-time dependence is universal, in the sense that it is specified by data
of the equilibrium universality class. The global limit shape in the variable
changes with the initial condition. In systems with more than two ground
states the tuning of an interaction parameter can induce a transition which is
the nonequilibrium quantum analog of the interfacial wetting transition
occurring in classical systems at equilibrium. We illustrate the general
results through the examples of the Ising, Potts and Ashkin-Teller chains.Comment: 18 pages, 5 figures. Published versio
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