The infinitestate Potts model and solid partitions of an integer
Abstract
It has been established that the infinitestate Potts model in d dimensions generates restricted partitions of integers in d {minus} 1 dimensions, the latter a wellknown 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. Closedform 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:

 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):
 CONF9603223
Journal ID: IJPBEV; ISSN 02179792; TRN: IM9719%%93
 Resource Type:
 Journal Article
 Journal Name:
 International Journal of Modern Physics B
 Additional Journal Information:
 Journal Volume: 11; Journal Issue: 12; 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 infinitestate 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 infinitestate 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 infinitestate Potts model and solid partitions of an integer". United States. https://doi.org/10.1142/S0217979297000150.
@article{osti_462623,
title = {The infinitestate Potts model and solid partitions of an integer},
author = {Huang, H Y and Wu, F Y},
abstractNote = {It has been established that the infinitestate Potts model in d dimensions generates restricted partitions of integers in d {minus} 1 dimensions, the latter a wellknown 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. Closedform 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 = 12,
volume = 11,
place = {United States},
year = {1997},
month = {1}
}