Showing papers by "Julia M. Yeomans published in 1981"
TL;DR: In this paper, the finite-size renormalisation group technique was applied to the directed percolation problem and the decay of correlations is anisotropic in this model and finite size scaling was extended to treat such anisotropy.
Abstract: The finite-size renormalisation group technique introduced by Nightingale (1976) is applied to the directed percolation problem. The decay of correlations is anisotropic in this model and finite-size scaling is extended to treat such anisotropy. Precise estimates for critical exponents and percolation probabilities are obtained for site, bond and site-bond percolation on the square lattice with bonds directed along the positive axes. Both free boundary conditions for which the results converge linearly with 1/n as n to infinity , and helical boundary conditions, for which, unexpectedly, the results converge linearly with 1/n3, are considered.
100 citations
TL;DR: In this paper, the global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for two-dimensional lattices using a Migdal-Kadanoff recursion relation.
Abstract: The global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for two-dimensional lattices using a Migdal-Kadanoff recursion relation It differs in important qualitative respects from the corresponding mean-field phase diagram The set of fixed points and flows provides the characteristic phase diagrams of the three-state Potts multicritical point and the ordinary ($n=1$) tricritical point in a complete set of symmetry-breaking fields The latter is associated, in this renormalization-group scheme, with seven distinct critical fixed points, a number which is surprisingly large
55 citations
TL;DR: The phase diagram of the uniaxial three-state chiral Potts or asymmetric clock model at low temperatures was calculated for dimensions d>2, using systematic series expansions carried to indefinitely high order as mentioned in this paper.
Abstract: The phase diagram of the uniaxial three-state chiral Potts or asymmetric clock model at low temperatures is calculated for dimensions d>2, using systematic series expansions carried to indefinitely high order. The model exhibits two arbitrarily long sequences of distinct commensurate phases with (mean) wavevectors q= pi /3a and q=2 pi j/3(2j+or-1)a for j=1,2,3,...,jmax with jmax approximately= square root 2 ln(1+ square root 2) exp(3J/2kBT) to infinity as T to 0.
33 citations
32 citations
22 citations
TL;DR: In this paper, a class of decorated spin 1/2 Ising models is introduced: all bonds of a hypercubic lattice parallel to one axis are decorated by n spins.
Abstract: A class of decorated spin 1/2 Ising models is introduced: all bonds of a hypercubic lattice parallel to one axis are decorated by n spins. Within each decorated bond, nearest neighbor ferromagnetic interactions compete with next‐nearest neighbor antiferromagnetic interactions. An exact dedecoration transformation reduces the model to an anisotropic Ising model which is exactly soluble in two dimensions (d = 2) and for which accurate series expansion estimates are available for d = 3. Phase diagrams are presented for d = 2 and 3 : all exhibit a multiphase point at which many distinct, spatially modulated commensurate phases coexist. The variation of the characteristic wavevector and other properties are compared and contrasted with those of the axial next‐nearest neighbor Ising (ANNNI) models.
2 citations