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Title: The infinite-state Potts model and solid partitions of an integer

Abstract

It has been established that the infinite-state Potts model in d dimensions generates restricted partitions of integers in d {minus} 1 dimensions, the latter a well-known intractable problem in number theory for d > 3. Here the authors consider the d = 4 problem. They consider a Potts model on an L x M x N x P hypercubic lattice whose partition function G{sub L M N P}(t) generates restricted solid partitions on an L x M x N lattice with each part no greater than P. Closed-form expressions are obtained for G{sub 222P} (t) and the authors evaluated its zeros in the complex t plane for different values of P. On the basis of their numerical results they conjecture that all zeros of the enumeration generating function G{sub L M N P}(t) lie on the unit circle {vert_bar}t{vert_bar} = 1 in the limit that any of the indices L, M, N, P becomes infinite.

Authors:
;  [1]
  1. Northeastern Univ., Boston, MA (United States). Center for Interdisciplinary Research in Complex Systems
Publication Date:
Sponsoring Org.:
National Science Foundation, Washington, DC (United States)
OSTI Identifier:
462623
Report Number(s):
CONF-9603223-
Journal ID: IJPBEV; ISSN 0217-9792; TRN: IM9719%%93
Resource Type:
Journal Article
Journal Name:
International Journal of Modern Physics B
Additional Journal Information:
Journal Volume: 11; Journal Issue: 1-2; Conference: Exactly soluble models in statistical mechanics: Current status and historical perspectives, Boston, MA (United States), Mar 1996; Other Information: PBD: 20 Jan 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; CRYSTAL MODELS; PARTITION FUNCTIONS; STATISTICAL MECHANICS; NUMERICAL SOLUTION; PHASE TRANSFORMATIONS

Citation Formats

Huang, H Y, and Wu, F Y. The infinite-state Potts model and solid partitions of an integer. United States: N. p., 1997. Web. doi:10.1142/S0217979297000150.
Huang, H Y, & Wu, F Y. The infinite-state Potts model and solid partitions of an integer. United States. https://doi.org/10.1142/S0217979297000150
Huang, H Y, and Wu, F Y. Mon . "The infinite-state Potts model and solid partitions of an integer". United States. https://doi.org/10.1142/S0217979297000150.
@article{osti_462623,
title = {The infinite-state Potts model and solid partitions of an integer},
author = {Huang, H Y and Wu, F Y},
abstractNote = {It has been established that the infinite-state Potts model in d dimensions generates restricted partitions of integers in d {minus} 1 dimensions, the latter a well-known intractable problem in number theory for d > 3. Here the authors consider the d = 4 problem. They consider a Potts model on an L x M x N x P hypercubic lattice whose partition function G{sub L M N P}(t) generates restricted solid partitions on an L x M x N lattice with each part no greater than P. Closed-form expressions are obtained for G{sub 222P} (t) and the authors evaluated its zeros in the complex t plane for different values of P. On the basis of their numerical results they conjecture that all zeros of the enumeration generating function G{sub L M N P}(t) lie on the unit circle {vert_bar}t{vert_bar} = 1 in the limit that any of the indices L, M, N, P becomes infinite.},
doi = {10.1142/S0217979297000150},
url = {https://www.osti.gov/biblio/462623}, journal = {International Journal of Modern Physics B},
number = 1-2,
volume = 11,
place = {United States},
year = {1997},
month = {1}
}