Universal amplitude ratios in the Ising model in three dimensions

Abstract

We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A + /A − in the three-dimensional Ising model via the impact angle φ of complex temperature zeros. We also measure the correlationlength critical exponent ν from finite-size scaling, and the specific-heat exponent α through hyperscaling. Extrapolations to the thermodynamic limit yield φ = 59.2(1.0) • , A + /A − = 0.56(3), ν = 0.63048(32) and α = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.

Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations

“…It well agrees with the other value ω = 1.171(96) reported here. Searching for a different method, we have evaluated the Fisher zeros of partition function from MC simulations by the Wolff single cluster algorithm, following the method described in [10]. The results for 4 ≤ L ≤ 72 have been reported in [10].…”

“…Searching for a different method, we have evaluated the Fisher zeros of partition function from MC simulations by the Wolff single cluster algorithm, following the method described in [10]. The results for 4 ≤ L ≤ 72 have been reported in [10]. We have performed high statistics simulations (with MC measurements after each max{2, L/4} Wolff clusters, omitting 10 6 measurements from the beginning of each simulation run, and totally 5 × 10 8 measurements used in the analysis for each L) for 4 ≤ L ≤ 128.…”

“…6. We have reached it by using the results of [10] and finite-size extrapolations. We have also estimated the second zeros for L = 4, 32, 64 from different simulation runs -see Tab.…”

“…3.0638 (15) Here u c = exp(−4β c ) is the critical u value, corresponding to the critical coupling β c . The estimation of correction-to-scaling exponent ω from fits of Ψ 1 (L) to A + BL −ω has been considered in [10], assuming the known approximate value 0.2216546 of β c . The use of Ψ 2 (L) instead of Ψ 1 (L) is another method, which has an advantage that it does not require the knowledge of the critical coupling β c .…”

Zeros in Partition Function and Critical Behavior of Disordered Three Dimensional Ising Model

“…Nevertheless we can study the transition in a finite system by analytical continuation to complex temperatures, β = η + iξ. In this case the partition function includes both oscillating and damping factors [10]:…”