Monte Carlo study of the two-dimensional site-diluted dipolar Ising model

TL;DR

This study uses tempered Monte Carlo simulations to analyze the phase transitions and critical behavior of a 2D site-diluted dipolar Ising model, revealing a critical concentration and the nature of the paramagnetic phase.

Contribution

It provides the first detailed Monte Carlo analysis of the phase diagram and critical properties of the 2D site-diluted dipolar Ising system, including estimates of critical exponents.

Findings

Existence of a critical concentration x_c=0.79(5) for antiferromagnetic order.

Paramagnetic phase persists for all T>0.

Estimated critical exponent 1/nu=0.35(10).

Abstract

By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a square lattice, and point along a common crystalline axis. For x_c< x<=1, where x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which vanishes as x approaches x_c from above. At lower values of x, we study (i) distributions of the spin--glass (SG) overlap q, (ii) their relative mean square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG correlation length. From their variation with temperature and system size, we find that the paramagnetic phase covers the entire T>0 range. Our results enable us to obtain an estimate of the critical exponent associated to the correlation length at T=0, 1/nu=0.35(10).