High-temperature series expansions for random Potts models
نویسندگان
چکیده
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 parameters. We present analyses of the new series for the susceptibility of the Ising (q = 2) and 4-state Potts model in three dimensions up to the order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.
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 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 کاملHigh-temperature series expansions for the q-state Potts model on a hypercubic lattice and critical properties of percolation.
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 ...
متن کاملFunctional relations for the order parameters of the chiral Potts model: low-temperature expansions
This is the third in a series of papers in which we set up and discuss the functional relations for the “split rapidity line” correlation function in the N–state chiral Potts model. The order parameters of the model can be obtained from this function. Here we consider the case N = 3 and write the equations explicitly in terms of the hyperelliptic functions parametrization. We also present four-...
متن کامل