Random Field Models for Relaxor Ferroelectric Behavior

TL;DR

This study uses Monte Carlo simulations to explore a four-state clock model with random fields, revealing complex ground states and glassy dynamics relevant to relaxor ferroelectric behavior.

Contribution

It introduces a coupled Ashkin-Teller-like model with random fields, showing novel ground states and phase transition characteristics in relaxor ferroelectric systems.

Findings

Ground states depend on the ratio D/J, with distinct ordered and disordered phases.

A large peak in structure factor indicates glassy dynamics above the transition.

Phase transition appears first order with small latent heat.

Abstract

Heat bath Monte Carlo simulations have been used to study a four-state clock model with a type of random field on simple cubic lattices. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $D$ to one of the four spin states, chosen randomly at each site. This Ashkin-Teller-like model does not separate; the two random-field Ising model components are coupled. When $D / J = 3$, the ground states of the model remain fully aligned. When $D / J \ge 4$, a different type of ground state is found, in which the occupation of two of the four spin states is close to 50%, and the other two are nearly absent. This means that one of the Ising components is almost completely ordered, while the other one has only short-range correlations. A large peak in the structure factor $S (k)$ appears at small $k$ for temperatures well above the transition to long-range order, and the appearance of this peak is associated with slow, "glassy" dynamics. The phase transition into the state where one Ising component is long-range ordered appears to be first order, but the latent heat is very small.