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

doi:https://doi.org/10.1142/S0217979297000150

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

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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:

Huang, H Y; Wu, F Y ^[1]

Northeastern Univ., Boston, MA (United States). Center for Interdisciplinary Research in Complex Systems

Publication Date:: 1997-01-20

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.

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                    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

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                    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.

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@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}

}

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