arXiv:cond-mat/0504022 · Physical Review B

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

Farkas Adam Bagaméry, Loïc Turban, Ferenc Iglói

Published Sep 6, 2005• 10 citations

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, which has a correlator, $G(r)\ensuremath{\sim}{r}^{\ensuremath{-}1}$, 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 $\ensuremath{\nu}=2.005(5)$ corresponds to that expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density ${x}_{m}=\ensuremath{\beta}∕\ensuremath{\nu}=0.1294(7)$ is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.

DOI: 10.1103/physrevb.72.094202

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arXiv:cond-mat/0504022 · Physical Review B

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

Farkas Adam Bagaméry, Loïc Turban, Ferenc Iglói

Published Sep 6, 2005• 10 citations

arXiv HTML PDF

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, which has a correlator,

G(r)\ensuremath{\sim}{r}^{\ensuremath{-}1}

, 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

\ensuremath{\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}=\ensuremath{\beta}∕\ensuremath{\nu}=0.1294(7)

is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.

DOI: 10.1103/physrevb.72.094202

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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, which has a correlator,

G(r)\ensuremath{\sim}{r}^{\ensuremath{-}1}

\ensuremath{\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}=\ensuremath{\beta}∕\ensuremath{\nu}=0.1294(7)

is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.

p

increases from 0 to 0.95, at the associated quantum phase transitions the numerical value of the correlation length exponent $\ensuremath{\nu}$ grows from a number compatible with the

O(3)

result 0.7112(5) to a number slightly greater than 1. In other words, by varying

p

, $\ensuremath{\nu}$ can reach an outcome between 0.7112(5) and 1 (or greater). Furthermore, among the studied values of

p

, all the associated $\ensuremath{\nu}$ violate the Harris criterion except the ones corresponding to $p\ensuremath{\ge}0.9$. Considering the form of the employed disorder here, the above described scenario should remain true for other randomness if it is based on an idea similar to the one used in this study. This is indeed the case according to our preliminary results stemming from investigating another disorder distribution.

0.995<a<2

and is characterized by the correlation length exponent $\ensuremath{\nu}=2/a+O({(2\ensuremath{-}a)}^{3})$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent ${\ensuremath{\eta}}_{2}=1/2\ensuremath{-}(2\ensuremath{-}a)/4+O({(2\ensuremath{-}a)}^{2})$.

(n=1)

, and others. In addition, for

q=8

, we find that there is only a single correlation length exponent $\ensuremath{\nu}$ describing the correlation length away from criticality. This is numerically very close to the pure Ising value $\ensuremath{\nu}=1$.