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 appli… Show more
“…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.…”
Section: Multiple Plateauxmentioning
confidence: 83%
“…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].…”
We present a new scheme for extracting approximate values in "the improved perturbation method", which is a sort of resummation technique capable of evaluating a series outside the radius of convergence.We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the "plateau" structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively.We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.
“…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.…”
Section: Multiple Plateauxmentioning
confidence: 83%
“…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].…”
We present a new scheme for extracting approximate values in "the improved perturbation method", which is a sort of resummation technique capable of evaluating a series outside the radius of convergence.We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the "plateau" structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively.We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.
“…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.…”
Section: Resultsmentioning
confidence: 99%
“…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.…”
Section: The Improved Perturbation Theorymentioning
confidence: 99%
“…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.…”
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It also gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua.
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