Proposal of a Checking Parameter in the Simulated Annealing Method Applied to the Spin Glass Model

We propose a checking parameter utilizing the breaking of the Jarzynski equality in the simulated annealing method using the Monte Carlo method. This parameter is based on the Jarzynski equality. By using this parameter, to detect that the system is in global minima of the free energy under gradual temperature reduction is possible. Thus, by using this parameter, one is able to investigate the efficiency of annealing schedules. We apply this parameter to the +-J Ising spin glass model. The application to the Gaussian Ising spin glass model is also mentioned. We discuss that the breaking of the Jarzynski equality is induced by the system being trapped in local minima of the free energy. By performing Monte Carlo simulations of the +-J Ising spin glass model and a glassy spin model proposed by Newman and Moore, we show the efficiency of the use of this parameter.Comment: 14 pages, 2 figures. v6: this is the final versio

A curious relationship between Potts glass models

A Potts glass model proposed by Nishimori and Stephen[H. Nishimori and M. J. Stephen, Phys. Rev. B 27, 5644 (1983)] is analyzed by means of the replica mean field theory. This model is a discrete model, has a gauge symmetry, and is called the Potts gauge glass model. By comparing the present results with the results of the conventional Potts glass model, we find the coincidences and differences between the models. We find a coincidence that the property for the Potts glass phase in this model is coincident with that in the conventional model at the mean field level. We find a difference that, unlike in the case of the conventional $p$-state Potts glass model, this system for large $p$ does not become ferromagnetic at low temperature under a concentration of ferromagnetic interaction. The present results support the act of numerically investigating the present model for study of the Potts glass phase in finite dimensions.Comment: 8 pages, 1 figure. v3: this is the final versio

The Derivation of the Exact Internal Energies for Spin Glass Models by Applying the Gauge Theory to the Fortuin-Kasteleyn Representation

We derive the exact internal energies and the rigorous upper bounds of specific heats for several spin glass models by applying the gauge theory to the Fortuin-Kasteleyn representation which is a representation based on a percolation picture for spin-spin correlation. The results are derived on the Nishimori lines which are special lines on the phase diagrams. As the spin glass models, the +-J Ising model and a Potts gauge glass model are studied. The present solutions agree with the previous solutions. The derivation of the solutions by the present method must be useful for understanding the relationship between the percolation picture for spin-spin correlation and the physical quantities on the Nishimori line.Comment: 10 pages, no figures. v3: minor corrections/addition

Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the Edwards-Anderson Ising Model on Complex Networks

We analytically show the percolation thresholds of the Fortuin-Kasteleyn cluster for the Edwards-Anderson Ising model on random graphs with arbitrary degree distributions. The results on the Nishimori line are shown. We obtain the results for the +-J model, the diluted +-J model, and the Gaussian model, by applying an extension of a criterion for the random graphs with arbitrary degree distributions. The results for the infinite-range $\pm J$ model and the Sherrington-Kirkpatrick model are also shown.Comment: 16 pages, 4 figures. v4: minor corrections/addition

Challenges Facing International Students in Writing Academic Essays

The current international situation is reflected in our educational settings, where increasing numbers of students study across the boundaries of countries. Large numbers of international students are especially involved in higher education. This paper illustrates what kind of difficulties students from non-English speaking backgrounds have in writing academic essays, one of the compulsory assignments in most anglophone higher education, by using three categories : culture, content and language. This also leads to a discussion of how these students might be helped to overcome these difficulties. In conclusion, some suggestions about the need for collaborative academic environments and institutional support, such as pre-sessional courses, are made