Logarithmic corrections to gap scaling in random-bond Ising strips

Abstract

Abstract. Numerical results for the first gap of the Lyapunov spectrum of the selfdual random-bond Ising model on strips are analysed. It is shown that finite-width corrections can be fitted very well by an inverse logarithmic form, predicted to hold when the Hamiltonian contains a marginal operator.

Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach

“…From this we can conclude that the exponent η does not depend on disorder, a result which has been known already 20,21,9,41,11 but without the precision shown above. Note that the correlation length ξ extracted from the ratio of TM eigenvalues (Eq.…”

“…In the off-critical Monte Carlo study of Talapov and Shchur 8 , bond disorder was observed to lead to increased values for the magnetization and susceptibility exponents β and γ, while the behaviour of the specific heat showed good agreement with the double logarithmic form (11). Together with the Rushbrooke equality α + 2β + γ = 2, these findings embody an inconsistency from which the authors concluded that their increased values for β and γ cannot be asymptotic.…”

“…These models have been widely studied, both because the corresponding pure system is well understood and because they constitute a marginal case in the Harris criterion 1 which assesses whether disorder constitutes a relevant or irrelevant perturbation for the critical behaviour of the pure system. For models of this type, the discussion currently appears to narrow down on two conflicting scenarios, namely the logarithmic corrections [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] versus the weak universality [18][19][20][21] scenario, though a broader spectrum of alternatives had been discussed earlier [22][23][24] (the interested reader will find a comprehensive report on the literature up to approximately 1982 in an early review by Stinchcombe 25 ). We will describe these scenarios and discuss these (and related) results in greater detail later on.…”

“…with the same critical exponents) as that of the pure 2d Ising model. These findings are almost all concerned with the ferromagnetic bond disordered situation, either theoretically, [3][4][5]17 or via numerical 6,7,[9][10][11][12][13][14]16 and series expansion 15 approaches, but the comparison with the spin diluted model is possible supposing -as it is generally believed to be the case -that the two systems are in the same universality class. 25,17 In discussing our results, we have to address two main issues.…”

Universality, frustration, and conformal invariance in two-dimensional random Ising magnets

“…21,23,29,32,34 Nonetheless, for dϭ2 unfrustrated disordered Ising systems they have turned out to be numerically very close, 23,29 at least at the critical point ͑see below for remarks on low-temperature behavior in the present case͒; significant differences arise only in the corrections to scaling, which are relevant for extrapolation to the thermodynamic limit. 34 In Refs. 10,11, the model considered here was studied with the aid of typical correlation lengths typ also calculated on strip geometries, but disregarding corrections to scaling; below, we will comment on some of the differences between our results and theirs.…”