Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model

TL;DR

This study uses tempered Monte Carlo simulations to explore the phase behavior of site-diluted dipolar Ising models, revealing a spin-glass phase with quasi-long-range order below a certain temperature.

Contribution

It provides the first detailed Monte Carlo analysis of the spin-glass phase in site-diluted dipolar Ising systems, identifying the nature of order and phase transitions.

Findings

Identification of a spin-glass phase below T_{sg} proportional to x e_d

Evidence of quasi-long-range order in the spin-glass phase

Finite correlation length ratios indicating non-exponential decay

Abstract

By tempered Monte Carlo simulations, we study site-diluted Ising systems of magnetic dipoles. All dipoles are randomly placed on a fraction x of all L^3 sites of a simple cubic lattice, and point along a given crystalline axis. For x_c< x<=1, where x_c = 0.65, we find an antiferromagnetic phase below a temperature which vanishes as x tends to x_c from above. At lower values of x, we find an equilibrium spin-glass (SG) phase below a temperature given by k_B T_{sg} = x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy. We study (a) the relative mean square deviation D_q^2 of |q|, where q is the SG overlap parameter, and (b) xi_L/L, where xi_L is a correlation length. From their variation with temperature and system size, we determine T_{sg}. In the SG phase, we find (i) the mean values <|q|> and <q^2> decrease algebraically with L as L increases, (ii) double peaked, but wide, distributions of q/<|q|> appear to be independent of L, and (iii) xi_L/L rises with L at constant T, but extrapolations to 1/L -> 0 give finite values. All of this is consistent with quasi-long-range order in the SG phase.