Crossover between displacive and order-disorder phase transition

TL;DR

This paper investigates the phase transition in a 3D anharmonic oscillator model, bridging displacive and order-disorder types, using Monte Carlo simulations and analytical approximations to understand transition temperatures and order parameters.

Contribution

It introduces a unified model parameter that smoothly connects displacive and order-disorder transitions, and develops an approximation scheme that accurately predicts transition temperatures.

Findings

Monte Carlo results agree with known asymptotic values for small and large parameters.

The new approximation scheme predicts transition temperatures within 5% accuracy.

The model provides a continuous crossover between displacive and order-disorder phase transitions.

Abstract

The phase transition in a 3D array of classical anharmonic oscillators with harmonic nearest-neighbour coupling (discrete $\phi^4$ model) is studied by Monte Carlo (MC) simulations and by analytical methods. The model allows to choose a single dimensionless parameter a determining completely the behaviour of the system. Changing a from 0 to $+\infty$ allows to go continuously from the displacive to the order-disorder limit. We calculate the transition temperature $T_c$ and the temperature dependence of the order parameter down to T=0 for a wide range of the parameter a. The $T_c$ from MC calculations shows an excellent agreement with the known asymptotic values for small and large a. The obtained MC results are further compared with predictions of the mean-field and independent-mode approximations as well as with predictions of our own approximation scheme. In this approximation, we introduce an auxiliary system, which yields approximately the same temperature behaviour of the order parameter, but allows the decoupling of the phonon modes. Our approximation gives the value of $T_c$ within an error of 5% and satisfactorily describes the temperature dependence of the order parameter for all values of a.