Scaling analysis of the site-diluted Ising model in two dimensions

Abstract

A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.

Site-diluted Ising model in four dimensions

“…Certain combinations of thermodynamic functions achieve this, but it turns out that FSS does this also. FSS therefore offers an ideal method to determine the exponents of the logarithmic corrections numerically [2].…”

“…If α < 0 in the pure system, then this type of disorder does not alter critical behaviour and the critical exponents are unchanged in the random system. In the two-dimensional case, the controversy concerns the strong universality hypothesis which maintains that the leading critical exponents remain the same as in the pure case and the weak universality hypothesis, which favours dilutiondependent leading critical exponents (see [2] and references therein).…”

“…However, unusual corrections to scaling characterise this model, and the precise nature of these corrections has been debated. This debate motivates the work presented herein: methods similar to those employed in [2], namely a high-statistics Monte Carlo approach coupled with finite-size scaling (FSS), are used to progress our understanding of the four-dimensional version of the random-site Ising model (RSIM).…”

Dynamic approach to finite-temperature magnetic phase transitions in the extendedJ1−J2model with vacancy order

“…In general, the vacancies would lead to a reduction in the transition temperature [47]. Magnetic frustration induced by the antiferromagnetic NNN interaction will also decrease the transition temperature [49].…”

“…Secondly, while the intralayer magnetic interactions J 1 and J 2 in A y Fe 2−x Se 2 are comparable to those in iron pnictides [44] as well as in AFe 2 Se 2 without vacancies [45,46], the interlayer magnetic coupling is very small [28] and is not sufficient to account for the enhancement of T N . Thirdly, it is well-known that uniformly and randomly distributed vacancies in spin systems always lead to a reduction of transition temperatures such as in the randomly site-diluted Ising model [47]. Therefore, detailed calculations are required to understand why and how the opposite tendency could appear in the A y Fe 2−x Se 2 compounds.…”