| Project/Area Number |
25610108
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Nara Medical University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
OTSUKA Hiromi 首都大学東京, 大学院理工学研究科, 助教 (10254145)
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| Research Collaborator |
FUJIMOTO Yoshio 奈良県立医科大学, 医学部, 教授 (90192731)
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| Project Period (FY) |
2013-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 統計力学 / 数理物理 / 格子模型 / 相関関数 / 平衡形 / 代数曲線 / シミュレーション |
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| Outline of Final Research Achievements |
In previous studies it was shown that asymptotic behavior of the (two-point) correlation function is expressed in terms of simple algebraic curves of genus 1 for two-dimensional solvable models.
Reexamining the eight-vertex model, we performed Monte Carlo simulations to investigate the correlation function of the Potts model; note that at the phase transition point the model is equivalent to the six-vertex model. Above the phase transition point we found essentially the same algebraic curves as the eight-vertex model. It was strongly suggested that the algebraic curves are quite general ones which represent the correlation functions of a wide class of lattice models, including unsolvable ones.
It was shown that the algebraic curves can be derived from the point group C_4v or C_6v. We pointed out a relation between the birational geometry and the (weak) universality hypothesis of critical phenomena.
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