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- W2023576663 abstract "I investigate the continuum limit of Klauder's field-theory models defined on a hypercubic lattice in four dimensions by mapping this problem onto a statistical-mechanical problem of an analog spin system, with partition function $Z=ensuremath{int}{ensuremath{-}ensuremath{infty}}^{ensuremath{infty}}ensuremath{Pi}{x}^{}[(frac{d{S}_{x}}{{|{S}_{x}|}^{B}})]mathrm{exp}(ensuremath{-}Aensuremath{Sigma}{x}^{}{{S}_{x}}^{2}ensuremath{-}{u}_{0}ensuremath{Sigma}{x}^{}{{S}_{x}}^{4}+Kifmmodetimeselsetexttimesfi{}ensuremath{Sigma}{x,ensuremath{mu}}^{}{S}_{x}{S}_{x+ensuremath{mu}})$ and $A$ a given function of ${u}_{0}$ and $B$ determined from an appropriate normalization condition. Monte Carlo methods are used to determine the phase diagrams and qualitative features of transitions in the regime $0ensuremath{le}B<1$, and in particular the behavior of the renormalized coupling constant ${g}_{R}$. For $B>0$ we find a line of first-order transitions for small ${u}_{0}$, while for larger values of ${u}_{0}$ there is a line of second-order transitions very similar to the Ising-type transitions of the usual ($B=0$) theory, and characterized by vanishing of the renormalized coupling ${g}_{R}$. Only in the latter case can the continuum field theory be defined, and it appears to be trivial free field theory for any choice of the parameter $B$." @default.
- W2023576663 created "2016-06-24" @default.
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- W2023576663 date "1983-09-15" @default.
- W2023576663 modified "2023-09-25" @default.
- W2023576663 title "Monte Carlo study of scale-covariant field theories" @default.
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- W2023576663 doi "https://doi.org/10.1103/physrevd.28.1461" @default.
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