Partial order in a frustrated Potts model

TL;DR

This study explores a 4-state frustrated Potts model on a 3D lattice, revealing an unconventional first-order phase transition with partial ordering and residual entropy, inspired by structural transitions in a pyrochlore oxide.

Contribution

It introduces a novel 4-state Potts model with geometrical frustration exhibiting partial order and residual entropy, analyzed via Wang-Landau Monte Carlo simulations.

Findings

Unconventional first-order phase transition observed.

Partial ordering with layered structure.

Large residual entropy at zero temperature.

Abstract

We investigate a 4-state ferromagnetic Potts model with a special type of geometrical frustration on a three dimensional diamond lattice by means of Wang-Landau Monte Carlo simulation motivated by a peculiar structural phase transition found in $\beta$-pyrochlore oxide KOs$_2$O$_6$. We find that this model undergoes unconventional first-order phase transition; half of the spins in the system order in a two dimensional hexagonal-sheet-like structure, while the remaining half stay disordered. The ordered sheets and the disordered sheets stack one after another. We obtain a fairly large residual entropy at $T = 0$ which originates from the disordered sheets.