Zeros of partition function for -symmetric model on square lattice-particular case

Nik Aizad Nik Hasmi, . and Siti Fatimah Zakaria, . and Fatimah Abdul Razak, . (2024) Zeros of partition function for -symmetric model on square lattice-particular case. Journal of Sustainability Science and Management (Malaysia), 19 (6). pp. 1-14. ISSN 2672-7226

We study a statistical mechanics model of multiple-phase transition called the-symmetric model on the square lattice for five possible spin directions (). This study aims to investigate the existence of phase transition(s) and discuss the distribution of partition function zeros on the complex-temperature plane. Some cases of energy list χ are considered where they are written in an arbitrary arrangement of integer numbers (usually in decreasing value due to the separation angle). The partition functions are computed using a transfer matrix approach, and their zeros are found numerically using the Newton-Raphson method. A Monte-Carlo Metropolis simulation is then performed to study the critical point of phase transition. The results are compared to the zeros distribution of the partition functions for the considered cases. Studying this generalised model is vital to mimic the system in the real world and to help experimental works use a more sustainable approach.

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Abstract

We study a statistical mechanics model of multiple-phase transition called the-symmetric model on the square lattice for five possible spin directions (). This study aims to investigate the existence of phase transition(s) and discuss the distribution of partition function zeros on the complex-temperature plane. Some cases of energy list χ are considered where they are written in an arbitrary arrangement of integer numbers (usually in decreasing value due to the separation angle). The partition functions are computed using a transfer matrix approach, and their zeros are found numerically using the Newton-Raphson method. A Monte-Carlo Metropolis simulation is then performed to study the critical point of phase transition. The results are compared to the zeros distribution of the partition functions for the considered cases. Studying this generalised model is vital to mimic the system in the real world and to help experimental works use a more sustainable approach.

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Item Type:	Article
AGROVOC Term:	models
AGROVOC Term:	mathematics
AGROVOC Term:	data analysis
AGROVOC Term:	simulation
AGROVOC Term:	algorithms
AGROVOC Term:	research
AGROVOC Term:	forecasting
Geographical Term:	Malaysia
Uncontrolled Keywords:	Square lattice
Depositing User:	Mr. Khoirul Asrimi Md Nor
Date Deposited:	09 Apr 2025 00:55
Last Modified:	09 Apr 2025 01:08
URI:	http://webagris.upm.edu.my/id/eprint/2542

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