Minimalistic real-space renormalization of Ising and Potts Models in two dimensions

Frontiers in Physics

Pruessner, Gunnar¹  Willis, Gary¹  Keelan, Jonathan² 

[1] Department of Mathematics, Imperial College London, London, UK;Department of Physical Sciences, The Open University, Milton Keynes, UK

关键词: Real space renormalization;    Potts Model;    critical exponents;    Ising Model;    Two dimensional lattice;    Numerical methods;   

DOI  :  10.3389/fphy.2015.00046

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

We introduce and discuss a real-space renormalization group (RSRG) procedure on very small lattices, which in principle does not require any of the usual approximations, e.g. a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4x4 to 2x2) and implemented for the Ising Model and the q=3,4,5 Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3% to 7% of the exact values. The 4-state Potts Model generates a third magnetic exponent which seems to be unknown in the literature. A number of questions about the meaning of certain exponents and the procedure itself arise from its use of symmetry principles and its application to the q=5 Potts Model.

【 授权许可】

CC BY