# Mean-field theory of orientational ordering in rigid rotor models with identical atoms: spin conversion and thermal equilibration

## TL;DR

This paper investigates the orientational phase behavior of coupled rotor models with nuclear spin restrictions, showing that intermediate spin conversion times effectively behave like instantaneous conversions in the thermodynamic limit, and analyzes entropy effects.

## Contribution

It introduces a mean-field approach for intermediate spin conversion times and demonstrates its equivalence to the instantaneous case in large systems, providing new insights into entropy and phase diagrams.

## Key findings

- Mean-field approach for intermediate spin conversion times matches the instantaneous case in the thermodynamic limit.
- Configurational entropy peaks at a certain temperature, shifting lower with increased order.
- Phase diagrams reveal the impact of spin conversion times on orientational ordering.

## Abstract

In coupled rotor models which describe identical rotating nuclei the nuclear spin states restrict the possible angular momenta of each molecule. There are two mean-field approaches to determining the orientational phase diagrams in such systems. In one the nuclear spin conversion times are assumed to be instantaneous in the other infinite. In this paper the intermediate case, when the spin conversion times are significantly slower than those of rotational time scales, but are not infinite on the time-scale of the experiment, is investigated. Via incorporation of the configurational degeneracy it is shown that in the thermodynamic limit the mean-field approach in the intermediate case is identical to the instantaneous spin conversion time approximation. The total entropy can be split into configurational and rotational terms. The mean-field phase diagram of a model of coupled rotors of three-fold symmetry is also calculated in the two approximations. It is shown that the configurational entropy has a maximum as a function of temperature which shifts to lower temperatures with increasing order.