Transverse Dynamics of Ising Models in One, Two and Three Lattice Dimensions

J. Florencio, Surajit Sen, Zhi-Xiong Cai

涼二 宮崎, Ryoji Miyazaki, 秀稔 西森 +2 more

L.L. Gonçalves, Roger James Elliott

Ryoji Miyazaki, Hidetoshi Nishimori, Gerardo Ortíz

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.

J. Oitmaa, Michael Plischke, T.A. Winchester

We derive the moments, at $T=\ensuremath{\infty}$, of the longitudinal spin-spin correlation function of the Ising model in a transverse field. The first 20 moments are obtained for the linear chain, the first 12 moments for the fcc lattice. We use a method of Nickel [J. Phys. C 7, 1719 (1914)] to construct the relaxation function and find excellent agreement with the exact results of Capel and Perk [Physica (Utrecht) 87A, 211 (1977)] in one dimension and extremely good convergence in three dimensions. Our method of analysis provides much better convergence than methods based on truncation of the continued-fraction representation.

Amit Dutta, G. Aeppli, Bikas K. Chakrabarti +3 more