Two-dimensional Ising model with self-dual biaxially correlated disorder

Abstract

We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended Harris criterion. Critical properties of the system are studied by large scale Monte Carlo simulations. The correlation length critical exponent, \nu=2.005(5), corresponds to that expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density, x_m=0.1294(7), is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.Comment: 10 pages, 11 figures, RevTeX4, published version, minor change

Explicit Renormalization Group for D=2 Random Bond Ising Model with Long-Range Correlated Disorder

“…The result is in agreement with [7]. A good numerical confirmation of this relation for the special choice of ρ = 1 2 can be found in [16]. Also the field renormalization would acquire an anomalous dimension which is defined through the asymptotic behavior of vertex function in the long wavelength limit as…”

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

“…Results of computer simulations in Ref. [48,51] support the analytic result ν = 2/a, whereas the critical exponents obtained in numerical studies in Refs. [49,50] deviate from this prediction raising the question about dependence of the critical exponents on the peculiarities of disorder distribution.…”

“…There are two complex conjugated eigenvalues: the red solid curve at the bottom is the real part and the blue curve at the top is the imaginary part. The dashed lines are the series expansions (51).…”

“…In order to verify this conjecture one needs a controllable method which does not rely on ε = 4 − d expansion with analytical continuation to ε = 2. Subsequently, these analytic results have been checked by numerical calculations [48][49][50][51]. In turn, these have not led so far to common agreement either.…”

Griffiths phase and critical behavior of the two-dimensional Potts models with long-range correlated disorder

“…The isotropy can be restored by an appropriate superposition of two McCoy-Wu models oriented in two different directions. A different magnetic critical behavior is then observed [22]. When algebraically decaying disorder correlations are introduced in the transverse direction of the McCoy-Wu model, the Weinrib-Halperin law ν = 2/a, where a is the disorder correlation exponent, is recovered [21].…”