Phase structure of lattice φ4 theory by variational cumulant expansion

An optimized perturbation expansion for a global O(2) theory

“…One check we used was to set in turn each of the fields to zero. The model then reduces to that of a single real field with a φ 4 interaction and we find that we reproduce the results of Wu et al [12] who used the same approach and an S 0 equivalent in this limit. They in turn showed that these results match lattice Monte Carlo calculations extremely well.…”

“…As described, the OPE is a very general method so not surprisingly it has been rediscovered several times in different guises, applied to very different applications, and appears under many different names; it is also known as the linear δ-expansion [7], action-variational approach [8], improved gaussian approximation [9], variational perturbation theory [10], method of self-similar approximation [11], or the variational cumulant expansion [12]. For instance the method has been to the evaluation of simple integrals [13,14,7], solving non-linear differential equations [15], quantum mechanics [16,17,18,9,7] to quantum field theory both in the continuum [9,10] and on a lattice [7,19,20,21,22,23,24,25,26,27,8,12].…”

“…Given that the Higgs sector causes new problems, it is worth considering pure Higgs models on the lattice in the context of OPE methods, effectively the zero gauge coupling limit of the gauged Higgs models rather than the infinite Higgs mass limit represented by the pure gauge models. However, we have found only a discussion of the real scalar model on the lattice using OPE method [12] rather than models with continuous global symmetries relevant to realistic gauged Higgs models.…”

“…The model has not been studied before using the OPE on the lattice and further the Higgs sector in this model is different from that used in [26,27] where only the modulus of the Higgs was required. Likewise the variational ansatz we choose here is more complicated with more variational parameters than that used in [12] or [26,27]. We also study different schemes to fix the variational parameters.…”

“…However we were unable to find any suitable solutions for the variational parameters when we tried to minimise the variation in the expectation values of the field with respect to the variational parameters. Therefore we reverted to the method used in [12], and in calculations of all expectation values we choose unphysical variational parameters, j φ , j ψ , k ± , which minimized the free energy for the same set of physical parameters m 2 , λ.…”