Minimalistic real-space renormalization of Ising and Potts Models in two dimensions
| Autor: | Jonathan Keelan, Gunnar Pruessner, Gary Willis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Materials Science (miscellaneous)
Biophysics General Physics and Astronomy Chiral Potts curve Renormalization symbols.namesake real-space renormalization Statistical physics Physical and Theoretical Chemistry Mathematical Physics Mathematics two dimensional lattices Physics Renormalization group lcsh:QC1-999 Ising Model Real space renormalization Quantum electrodynamics symbols Exponent Ising model critical exponents Numerical methods Two dimensional lattice Hamiltonian (quantum mechanics) Critical exponent Potts Model lcsh:Physics Potts model |
| Zdroj: | Frontiers in Physics, Vol 3 (2015) |
| Popis: | 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 (4 × 4 to 2 × 2) and implemented for the Ising Model and the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3–7% 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. |
| Databáze: | OpenAIRE |
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