Related papers: Hyperscaling breakdown and Ising Spin Glasses: the…
Numerical data on scaling of the normalized Binder cumulant and the normalized correlation length are shown for the Thermodynamic limit regime, first for canonical Ising ferromagnet models and then for a range of Ising spin glass models. A…
In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above…
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been…
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
Extensive simulations are made on Ising Spin Glasses (ISG) with Gaussian, Laplacian and bimodal interaction distributions in dimension four. Standard finite size scaling analyses near and at criticality provide estimates of the critical…
Three dimensional Ising model ferromagnets on different lattices with nearest neighbor interactions, and on simple cubic lattices with equivalent interactions out to further neighbors, are studied numerically. The susceptibility data for…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein {\it et…
The critical behavior of the Binder cumulant for Ising spin glasses in dimension four are studied through simulation measurements. Data for the bimodal interaction model are compared with those for the Laplacian interaction model. Special…
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with…
From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the…
Ising spin glass models with bimodal, Gaussian, uniform and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff…
We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group (FRG) for the critical behavior of the random field Ising model in a superfield…
It is often assumed that for treating numerical (or experimental) data on continuous transitions the formal analysis derived from the Renormalization Group Theory can only be applied over a narrow temperature range, the "critical region";…
We investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction, $J_{ij} = |\vec{r}_i -\vec{r}_j|^{-(d+\sigma)}$, where…