Critical Entropy of Quantum Heisenberg Magnets on Simple-Cubic Lattices

Abstract

We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using optimized extended ensemble quantum Monte Carlo simulations, we extract the entropy at the critical temperature for magnetic order from a finite-size scaling analysis. For the antiferromagnetic case, the critical entropy density equals 0.341(5)$k_B$, whereas for the ferromagnet, a larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results to estimates put forward recently in studies assessing means of realizing the antiferromagnetic Néel state in ultra-cold fermion gases in optical lattices.

3 pages, 2 figures; published version

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Interaction-Induced Adiabatic Cooling for Antiferromagnetism in Optical Lattices
• Trapping and cooling fermionic atoms into the Mott and Néel states
• Antiferromagnetic Order of Repulsively Interacting Fermions on Optical lattices
• Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems

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