arXiv subjects
Publications and source records attributed to K. Tabata.
The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $β^{50}$ for the free energy, to $β^{32}$ for the magnetic susceptibility and to $β^{29}$ for the second moment correlation length. The series are analyzed to give the precise value of the critical point and the critical exponents of the model.
We have calculated the large-$q$ series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the $q$-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of $10^2 - 10^4$ than the Monte Carlo simulations. From the large-$q$ series of the eigenvalues of the transfer matrix, we also find that the excited states form a continuum spectrum and there is no particle state at the first order phase transition point.
We have calculated the large-q expansion for the energy cumulants and the magnetization cumulants at the phase transition point in the two-dimensional q-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirms us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior not only of the energy cumulants but also of the magnetization cumulants for $q \to 4_+$.
We have calculated the large-$q$ expansion for the energy and magnetization cumulants at the first order phase transition point in the two-dimensional $q$-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give highly convergent estimates of the cumulants for $q>4$. The results confirm us the correctness of the conjecture by Bhattacharya {\em et al.} on the asymptotic behavior of the energy cumulants for $q \to 4_+$ and a similar new conjecture on the magnetization cumulants.
We have calculated the large-q expansion for the energy cumulants at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the cumulants for $q \to 4_+$.
We have calculated the large-$q$ expansion for the specific heat at the phase transition point in the two-dimensional $q$-state Potts model to the 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allows us to give highly convergent estimates of the specific heat for $q>4$ on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the specific heat for $q \to 4_+$.
The low-temperature series are calculated for the free energy, magnetization and susceptibility in the Q-state Potts model on the square lattice, using the improved algorithm of the finite lattice method. The series are obtained to the order of $z^{41}$ for each of Q=5-50, and the result of their Padé type analysis is compared with those of the large-Q expansion and the Monte Carlo simulations.
We have calculated the low-temperature series for the second moment of the correlation function in $d=3$ Ising model to order $u^{26}$ and for the free energy of Absolute Value Solid-on-Solid (ASOS) model to order $u^{23}$, using the finite-lattice method.
We extend low-temperature series for the second moment of the correlation function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using finite-lattice method, and combining with the series for the susceptibility we obtain the low-temperature series for the second-moment correlation length to $u^{23}$. An analysis of the obtained series by inhomogeneous differential approximants gives critical exponents $ 2ν^{\prime} + γ^{\prime} \approx 2.55 $ and $ 2ν^{\prime} \approx 1.27 $.