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

Isentropic Curves at Magnetic Phase Transitions