Phase Transitions and Lattice Systems

Jhao-Hong Peng, Fu-Jiun Jiang

Abstract It is widely believed that the phase transition for the four-state ferromagnetic Potts model on the square lattice is of pseudo-first order. Specifically, it is expected that first-order phase transition behavior is found on small lattices and that the true nature of the second-order phase transition only emerges with large system sizes. It is also intuitively expected that, for other geometries, the types of the associated phase transitions should be identical to that of the square lattice. However, after simulating more than 16 million spins for the four-state Potts model, we observe that a feature of the first-order phase transition persists on the square lattice. Additionally, a characteristic of the second-order phase transition already appears on a small honeycomb lattice. Indications of a pseudo-first-order phase transition were not found in our investigation. This suggests that a thorough analytic calculation may be required to develop a better understanding of the presented results.

Robert B. Israel

Jhao-Hong Peng, Fu-Jiun Jiang

It is widely believed that the phase transition for the four-state ferromagnetic Potts model on the square lattice is of the pseudo-first order. Specifically, it is expected that first-order phase transition behavior is found on small lattices and that the true nature of second-order phase transition only emerges with large system sizes. It is also intuitively expected that for other geometries, the types of the associated phase transitions should be identical to that of the square lattice. However, after simulating more than 16 million spins for the four-state Pott model, we observe that a feature of first-order phase transition persists on the square lattice. Additionally, a characteristic of second-order phase transition already appears on a small honeycomb lattice. Indications of a pseudo-first-order phase transition were not found in our investigation. This suggests that a thorough analytic calculation may be required to develop a better understanding of the presented results.

Lorenza Saitta, Attilio Giordana, Antoine Cornuéjols

Wolfhard Janke E

Libo Liang, Yuqing Wang, Qi Huang +3 more

Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.