Quantum effects in the renormalization group approach to phase transitions
- 7 August 1975
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 8 (15) , L309-L313
- https://doi.org/10.1088/0022-3719/8/15/001
Abstract
The renormalization group approach to critical phenomena is developed for quantum mechanical problems with non-commuting operators. Applying the theory to the spin 1/2 Ising model with a transverse field Gamma it is found that the critical exponents are those of the Ising model with Gamma =0 if the transition occurs at T>0. However, for transitions at T=0 the critical behaviour of the d-dimensional transverse system corresponds to that of the (d+1)-dimensional Ising model with Gamma =0, in agreement with series expansion predictions. At T=0 the dynamic, as well as static, critical behaviour is given by mean field theory for d>3.Keywords
This publication has 14 references indexed in Scilit:
- The one-dimensional Ising model with a transverse fieldPublished by Elsevier ,2004
- On the critical behaviour of anisotropic systemsJournal of Physics C: Solid State Physics, 1974
- Scaling Function for Critical ScatteringPhysical Review Letters, 1973
- Renormalization-Group Verification of Crossover with Respect to the Lattice Anisotropy ParameterPhysical Review B, 1973
- Critical Behavior of the Anisotropic-Vector ModelPhysical Review B, 1972
- Critical behaviour of the Ising modelPhysics Letters A, 1972
- The Ising model with a transverse field. I. High temperature expansionJournal of Physics C: Solid State Physics, 1971
- Scaling Laws for Dynamic Critical PhenomenaPhysical Review B, 1969
- Gaussian average method in the statistical theory of the Ising modelThe European Physical Journal A, 1963
- Calculation of Partition FunctionsPhysical Review Letters, 1959