1/s-expansion for generalized dimensions in a hierarchical s-state Potts model

A. H. Osbaldestin

doi:10.1088/0305-4470/28/20/023

1/s-expansion for generalized dimensions in a hierarchical s-state Potts model

A. H. Osbaldestin^*

^*Corresponding author for this work

School of Mathematics & Physics

Loughborough University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the s-state Potts model on the diamond hierarchical lattice for large s. We show that the generalized dimensions D_q of the density of zeros supported by the associated Julia set are given by D_q = 1 - (q - 1)|s|^-2/3/4 log 2+O(s^-1). The information dimension D₁ equals 1 to all orders.

Original language	English
Article number	023
Pages (from-to)	5951-5962
Number of pages	12
Journal	Journal of Physics A: Mathematical and General
Volume	28
Issue number	20
DOIs	https://doi.org/10.1088/0305-4470/28/20/023
Publication status	Published - 1 Dec 1995

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10.1088/0305-4470/28/20/023

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title = "1/s-expansion for generalized dimensions in a hierarchical s-state Potts model",

abstract = "We consider the s-state Potts model on the diamond hierarchical lattice for large s. We show that the generalized dimensions Dq of the density of zeros supported by the associated Julia set are given by Dq = 1 - (q - 1)|s|-2/3/4 log 2+O(s-1). The information dimension D1 equals 1 to all orders.",

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AB - We consider the s-state Potts model on the diamond hierarchical lattice for large s. We show that the generalized dimensions Dq of the density of zeros supported by the associated Julia set are given by Dq = 1 - (q - 1)|s|-2/3/4 log 2+O(s-1). The information dimension D1 equals 1 to all orders.

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U2 - 10.1088/0305-4470/28/20/023

DO - 10.1088/0305-4470/28/20/023

M3 - Article

AN - SCOPUS:21844513567

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 20

M1 - 023

ER -

1/s-expansion for generalized dimensions in a hierarchical s-state Potts model

Abstract

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