Improved Taylor Expansion Method in the Ising Model

Abstract

We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling expansion, even in the case of a phase transition. We determine the approximate value of the transition point using this scheme. In the presence of an external magnetic field, we find both stable and metastable physical states. * ) In Ref. 13) there appears a treatment of the application of the improved Taylor expansion method to the Ising model. Our arguments here extend and clarify the work given there. * ) One attempt to apply this method to non-abelian Yang-Mills theory can be found in Ref. 14).

Improved perturbation method and its application to the IIB matrix model

“…If each of them can be interpreted as a physical state, some correspond to stable vacua, while others to the unstable ones. This situation is realized in Ising model [22]. When we carry out the improved perturbation for the IIB matrix model, we expect that multiple plateaux are realized corresponding respectively to different vacua with different symmetry.…”

“…It is considered as a sort of variational method [13,14,15,16,17,18]. It has been successfully applied to various models [19,20,21,22], and applications to matrix models were done in Refs. [23,24,25].…”

Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory

“…In the case of a model which exhibits phase transition, distribution of extrema and the value of observables in a plateau region change drastically around a phase transition point [20]. Thus we examine the distributions of extrema of the improved series In this paper we sweep α and m 2 from 0.0 to 10.0.…”

“…Although we do not yet have a rigorous definition of plateaux, we could identify them by their properties investigated in [9,13,19,20] as follows. The ideal realization of the plateau may have such a property that the improved series is totally independent of the artificial parameters ξ 0 in a certain region.…”

“…The IMFA has been applied successfully to a number of models to yield nonperturbative results [9,10,11,12,13,14,16,17,18,19,20]. In particular, the IMFA was applied to the IIB matrix model first in Ref.…”