Applications of exact solutions and numerical techniques in lattice spin models to biological systems.

2015 Fiscal Year Final Research Report

• Project/Area Number: 24654121
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Nagoya University
• Principal Investigator: Minami Kazuhiko 名古屋大学, 多元数理科学研究科, 准教授 (40271530)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 可解模型 / 生物の数理モデル

Outline of Final Research Achievements

It is found that the Hamiltonian can be transformed into the free fermion system, and hence its partition function can be obtained exactly, provided that the operators of the Hamiltonian satisfy specific commutation relations. A solvable Hamiltonian and a transformation that diagonalize the Hamiltonian is obtained simultaneously from a series of operators which satisfy the condition. The one-dimensional XY model, the two-dimensional Ising model, and other composite countable number of quantum spin chains are diagonalized following this procedure. The equivalence between the two-dimensional Ising model and the one-dimensional XY model is generalized, and the quantum susceptibility of the random transverse Ising chain is obtained in a integral form.

Free Research Field

統計物理学・数理物理