Critical temperature of the Ising model with correlated disorder

Herrmanns, K.

doi:10.1016/s0378-4371(98)00608-6

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In three dimensions Monte Carlo simulations were performed in Refs. [13][14][15][16][17][18][19] while renormalization group techniques were used in Refs. [9,20].…”

Section: Introductionmentioning

confidence: 99%

Critical exponent $ν$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques

Kazmin,

Janke

2020

Preprint

View full text Add to dashboard Cite

We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a power-law r −a . We derive the critical exponent of the correlation length ν and the confluent correction exponent ω in dependence of a by combining different concentrations of defects 0.05 ≤ p d ≤ 0.4 into one global fit ansatz and applying finitesize scaling techniques. We simulate and study a wide range of different correlation exponents 1.5 ≤ a ≤ 3.5 as well as the uncorrelated case a = ∞ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent a and the concentrations of defects p d . We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: ν = 2/a and discuss the occurring deviations.

show abstract

“…In three dimensions Monte Carlo simulations were performed in Refs. [13][14][15][16][17][18][19] while renormalization group techniques were used in Refs. [9,20].…”

Section: Introductionmentioning

confidence: 99%