Perturbative PDF of the total magnetization of the 4D Ising model

2020/05/04 by Andrea Allais, Allais, Andrea
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.48550/arxiv.2005.01737

arxiv created 2020/05/04 · arxiv updated 2020/05/06

Abstract

We compute, at one loop in perturbation theory, the probability density function of the total magnetization M of the Ising model on the 4-torus and the 4-sphere. We develop a single perturbative expansion that is valid in the symmetric phase as well as the broken symmetry phase, provided that the correlation length is large compared to the system size L. We find that, at the critical point, for large system size in lattice units, the PDF approaches p(M)∼ exp(-f(L) M⁴). Consequently, the critical value of the Binder cumulant of the total magnetization is U = 1 - (4 Γ(5/4)²)/(3 Γ(3/4)²). We validate our results by comparison with Monte Carlo simulation.

Related

• Critical Probability Distributions of the order parameter at two loops I: Ising universality class
• The Magnetization of the 3D Ising Model
• Scaling, domains, and states in the four-dimensional random field Ising magnet
• Conformal invariance and the Ising model on a 3 sphere in connection with the Quantum Elemental Method
• Power-law correction in the probability density function of the critical Ising magnetization