Frustrated Ising model on the Cairo pentagonal lattice

TL;DR

This paper presents an exact solution for the pentagonal Ising model, revealing its phase diagram, phase transitions, and thermodynamic properties, including frustration effects and low-temperature behaviors.

Contribution

It provides a novel exact solution for the pentagonal Ising model and explores its phase diagram and thermodynamic properties, highlighting frustration and phase transitions.

Findings

Identified ferromagnetic, ferrimagnetic, and frustrated ground states.

Discovered phase transitions between FIM, disordered, and FM states.

Observed low entropy and specific heat near critical temperature.

Abstract

Through the direct decoration transformation approach, we obtain a general solution for the pentagonal Ising model, showing its equivalence to the isotropic free-fermion eight-vertex model. We study the ground-state phase diagram, in which one ferromagnetic (FM) state, one ferrimagnetic (FIM) state, and one frustrated state are found. Using the exact solution of the pentagonal Ising model, we discuss the finite-temperature phase diagrams and find a phase transition between the FIM state and the disordered state as well as a phase transition between the disordered state and the FM state. We also discuss some additional remarkable properties of the model, such as the magnetization, entropy, and specific heat, at finite temperature and at its low-temperature asymptotic limit. Because of the influence of the second-order phase transition between the frustrated and ferromagnetic phases, we obtain surprisingly low values of the entropy and the specific heat until the critical temperature is reached.