Low Dimensional Ordering on a Lattice Model

TL;DR

This paper introduces a lattice model capturing molecular orientation and frustration, revealing phase transitions and equivalences to known models, with a comprehensive mean field analysis and exact limits.

Contribution

It presents a new d-dimensional lattice model that generalizes molecular orientation behavior and connects to the Ising model for two dimensions.

Findings

Model equivalent to 2D Ising for d=2

Transition from isotropic to anisotropic phases for d>2

Mean field analysis aligns with exact limit properties

Abstract

A simple d-dimensional lattice model is proposed, incorporating some degree of frustration and thus capable of describing some aspects of molecular orientation in covalently bound molecular solids. For d=2 the model is shown to be equivalent to the standard two-dimensional Ising model, while for d>2 it describes a peculiar transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. A general mean field analysis is presented and compared to some exact limit properties.