Related papers: Series expansions without diagrams
The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described that…
We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous…
New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of…
A previously tested differential equation method for generating low temperature series expansion for diagonal spin-spin correlation functions in the d=2 Ising model is extended to generate the non-universal terms for arbitrary separation of…
A high temperature expansion is employed to map some complex anisotropic nonhermitian three and four dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. We also address the dimensional…
I present a modification of the shadow-lattice technique, which allows one to derive low temperature series for discrete spin models to high orders. Results are given for the 3-d Ising model up to 64 excited bonds, for the 4-d Ising model…
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…
The finite-lattice method of series expansions has been combined with a new extrapolation procedure to extend the low-temperature series for the specific heat, spontaneous magnetisation and susceptibility of the spin-1 Ising model on the…
High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these…
25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by…
We propose a computational method to obtain series expansions in powers of time for general dynamical systems described by a set of hierarchical rate equations. The method is generally applicable to problems in both equilibrium and…
We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincar\'e groups. Using these symmetries, we show that the intricate sums appearing in the…
The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic susceptibility and to…
We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of…
We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines.
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $3$-state Potts model on the simple cubic lattice to order $z^{43}$ and the…
We present a differential formulation of the recursion formula of the hierarchical model which provides a recursive method of calculation for the high-temperature expansion. We calculate the first 30 coefficients of the high temperature…
On simple cubic lattices, we compute low temperature series expansions for the energy, magnetization and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds respectively, and the eight-state Potts model…