High-temperature series expansions for the q-state Potts model on a hypercubic lattice and critical properties of percolation.
نویسندگان
چکیده
We present results for the high-temperature series expansions of the susceptibility and free energy of the q-state Potts model on a D-dimensional hypercubic lattice ZD for arbitrary values of q. The series are up to order 20 for dimension D1 limit of these series, we estimate the percolation threshold pc and critical exponent gamma for bond percolation in different dimensions. We also extend the 1/D expansion of the critical coupling for arbitrary values of q up to order D-9.
منابع مشابه
Random-bond Potts models on hypercubic lattices: high-temperature series expansions*
We derive high-temperature series expansions for the free energy and the susceptibility of random-bond qstate Potts models on hypercubic lattices using a stax-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic par...
متن کاملHigh-temperature series expansions for random-bond Potts models on Z
We use a star-graph expansion technique to compute high-temperature series for the free energy and susceptibility of randombond q-state Potts models on hypercubic lattices. This method allows us to calculate quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic parameters. This enables s...
متن کاملHigh-temperature series expansions for random Potts models
We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique, quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic paramet...
متن کاملStar-graph expansions for bond-diluted Potts models.
We derive high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic pa...
متن کاملJa n 20 05 Determinant of the Potts model transfer matrix and the critical point
By using a decomposition of the transfer matrix of the q-state Potts Model on a three dimensional m× n× n simple cubic lattice its determinant is calculated exactly. By using the calculated determinants a formula is conjectured which approximates the critical temperature for a d-dimensional hypercubic lattice. PACS numbers: 05.50.+q, 02.70.-c
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 74 5 Pt 1 شماره
صفحات -
تاریخ انتشار 2006