Some Algebraic Techniques for obtaining Low-temperature Series Expansions

Enting, I. G.

doi:10.1071/ph780515

Cited by 36 publications

(3 citation statements)

References 4 publications

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“…In the following we describe the method used to derive the series expansions [35,36]. The free energy can be derived from the ferromagnetic part Z (0) of the partition function.…”

Section: Critical Exponentsmentioning

confidence: 99%

Low temperature expansion of the gonihedric Ising model

Pietig

Wegner

1998

Nuclear Physics B

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We investigate a model of closed (d − 1)-dimensional soft-self-avoiding random surfaces on a d-dimensional cubic lattice. The energy of a surface configuration is given by E = J(n 2 + 4k n 4 ), where n 2 is the number of edges, where two plaquettes meet at a right angle and n 4 is the number of edges, where 4 plaquettes meet. This model can be represented as a Z 2 -spin system with ferromagnetic nearest-neighbour-, antiferromagnetic next-nearest-neighbour-and plaquette-interaction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaption of Peierls argument, we prove the existence of infinitely many ordered low temperature phases for the case k = 0. A low temperature expansion of the free energy in 3 dimensions up to order x 38 (x = e −βJ ) shows, that for k > 0 only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order x 44 for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results.

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“…In the following we describe the method used to derive the series expansions [35,36]. The free energy can be derived from the ferromagnetic part Z (0) of the partition function.…”

Section: Critical Exponentsmentioning

confidence: 99%

Low temperature expansion of the gonihedric Ising model

Pietig

Wegner

1998

Nuclear Physics B

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“…The approach here differs in details but is similar in essence to the combining of partition functions in the finite lattice method of Refs. [2] and [3].…”

Section: Cancelling Loopsmentioning

confidence: 99%

“…The method is based on a recursive transfer matrix procedure of Binder [1] for the explicit solution of discrete models on small lattices. Enting [2] discussed how to combine such solutions on small lattices to obtain low temperature series. Guttmann and Enting have pushed this finite lattice method to obtain rather high order low temperature series for the three dimensional Ising model [3].…”

Section: Introductionmentioning

confidence: 99%

Series expansions without diagrams

et al. 1994

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We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

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Triangular lattice Potts models

Enting

1982

J Stat Phys

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Some Algebraic Techniques for obtaining Low-temperature Series Expansions

Cited by 36 publications

References 4 publications

Low temperature expansion of the gonihedric Ising model

Low temperature expansion of the gonihedric Ising model

Series expansions without diagrams

Triangular lattice Potts models

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