| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1998: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1997: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1996: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Research Abstract |
Using the finite lattice method we calculated the high order terms of the various types of the parameter expansions for various kinds of spin systems.
We first calculated the low-temperature expansion series of the free energy, the magnetization and the magnetic susceptibility in the q-state Potts model in two dimensions for all of q=5-50, where the system exhibits first order phase transition to the 41st order in the expansion, parameter. We also applied the finite lattice method to the large-q expansion of the same system and obtained the series for the up to 6th order energy cumulants to the 23rd order in 1/√q. Analyzing the series, we found that the values of the free energy and the latent heat coincide in very high precision with those of the exact solutions at the critical point and the series for the specific heat gives converging results in the accuracy of a few percent even for q=5, where the correlation length of the system amount to several thousands of the lattice spacing and other methods such as the Monte Carlo simulations cannot give any meaningful result.
Secondly we calculated the low-temperature expansion series for the three kinds of quantities concerning the interface width for the Ising model in three dimensions and for the Absolute value SOS model and Discrete Gaussian model on the square lattice and on the triangular lattice, respectively, to 17th, 23rd, 22nd, 24th and 22nd order in the expansion parameter for the respective model. Assuming the critical exponent of the each quantity that is predicted by the renormalization group arguments, we obtained from the series the value of the roughening transition point for each model. They agree quite well with the results of the Monte Carlo simulation for the former three models and they give new prediction for the latter two models.
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