Isentropic Curves at Magnetic Phase Transitions

TL;DR

This paper investigates the behavior of isentropic curves during magnetic phase transitions in the Blume-Capel and Fermi Hubbard models using mean field and Monte Carlo methods, revealing how these curves interact with phase boundaries and temperature changes.

Contribution

It provides a detailed analysis of isentropic curves in magnetic transition models, highlighting their topology and interaction with phase boundaries under different conditions.

Findings

Isentropic curves in BCM often run parallel to phase boundary in low vacancy regime.

Adiabatic heating occurs when moving away from phase boundary.

FHM isentropes are simple in half-filled case but complex when doped.

Abstract

Experiments on cold atom systems in which a lattice potential is ramped up on a confined cloud have raised intriguing questions about how the temperature varies along isentropic curves, and how these curves intersect features in the phase diagram. In this paper, we study the isentropic curves of two models of magnetic phase transitions- the classical Blume-Capel Model (BCM) and the Fermi Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods are used. The isentropic curves of the BCM generally run parallel to the phase boundary in the Ising regime of low vacancy density, but intersect the phase boundary when the magnetic transition is mainly driven by a proliferation of vacancies. Adiabatic heating occurs in moving away from the phase boundary. The isentropes of the half-filled FHM have a relatively simple structure, running parallel to the temperature axis in the paramagnetic phase, and then curving upwards as the antiferromagnetic transition occurs. However, in the doped case, where two magnetic phase boundaries are crossed, the isentrope topology is considerably more complex.