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International Journal of Modern Physics A

THE OFF-CRITICAL BEHAVIOR OF THE MULTICRITICAL ISING MODELS

Marcio Jose Martins

Published Dec 20, 1992• 4 citations
Publisher

Abstract

The scaling region of the two-dimensional tetracritical and pentacritical Ising models is studied by using the truncated conformal approach. We compare the off-critical spectrum with the conjectured S matrices. In the case of the subleading thermal perturbation we discuss the phase shift measurement in different sectors of the theory. In the odd sector, we present evidence that it is necessary to introduce fractional quantum numbers in order to parametrize the canonical momentum. For the nonintegrable deformations, we make an analysis of the phase shift behavior near a resonance.

DOI
10.1142/s0217751x92003513

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The exact perturbation approach is used to derive the (seven) elementary correlation lengths and related mass gaps of the two-dimensional dilute A4 lattice model in regime 2− from the Bethe Ansatz solution. This model provides a realization of the integrable φ(1,2) perturbation of the c=710 conformal field theory, which is known to describe the off-critical thermal behavior of the tricritical Ising model. The E7 masses predicted from purely elastic scattering theory follow in the approach to criticality. Universal amplitudes for the tricritical Ising model are calculated.
The tricritical Ising model perturbed by the subleading energy operator [Formula: see text] was known to be an integrable scattering theory of massive kinks,14 and in fact it preserves supersymmetry. We consider here the model defined on the half-plane with a boundary and compute the associated factorizable boundary S matrix. The conformal boundary conditions of this model are identified and the corresponding S matrices are found. We also show how some of these S matrices can be perturbed and generate “flows” between different boundary conditions.
We explore the dynamical behavior at and near a special class of two-dimensional quantum critical points. Each is a conformal quantum critical point (CQCP), where in the scaling limit the equal-time correlators are those of a two-dimensional conformal field theory. The critical theories include the square-lattice quantum dimer model, the quantum Lifshitz theory, and a deformed toric code model. We show that under generic perturbation the latter flows toward the ordinary Lorentz-invariant (2+12+12+1)-dimensional Ising critical point, illustrating that CQCPs are generically unstable. We exploit a correspondence between the classical and quantum-dynamical behavior in such systems to perform an extensive numerical study of two lines of CQCPs in a quantum eight-vertex model or, equivalently, two coupled deformed toric codes. We find that the dynamical critical exponent zzz remains 2 along the U(1)-symmetric quantum Lifshitz line, while it continuously varies along the line with only Z2{\mathbb{Z}}_{2}Z2​ symmetry. This illustrates how two CQCPs can have very different dynamical properties, despite identical equal-time ground-state correlators. Our results equally apply to the dynamics of the corresponding purely classical models.
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