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- W2286847110 abstract "We give a brief pedagogical introduction to Markov chain Monte Carlo simulations of statistical systems and the basics of the $phi^4$ quantum field theory. We show how to treat $phi^4$ theory as a statistical system in Euclidean space and perform lattice simulations using both local and cluster Monte Carlo algorithms. We then present the details and results of simulations of $phi^4$ theory on the lattice in which we chart the phase transition line of the theory in two and four dimensions and calculate an accurate value of the continuum critical coupling constant in two dimensions. Finally we discuss lattice simulations that calculate the masses of $phi^4$ solitons in two dimensions, nonperturbative phenomena that result from the nonlinearity of the theory.The two-dimensional critical coupling constant we obtain is $left[lambda / mu^2right]_{crit} = 10.85^{+.03}_{-.08}$, which disagrees by over $7sigma$ with the value of $left[lambda / mu^2right]_{crit} = 10.26^{+.08}_{-.04}$ reported by Loinaz and Willey. We show that this disagreement is the result of higher-order dependence of $left[lambda / mu^2right]_{crit}$ on $lambda$, which is only revealed by our more extensive calculations and resulting increase in precision; our data is actually largely consistent with theirs. Our calculations of $phi^4$ soliton masses improve upon the previous study by Ciria and Taranc'on; although our simulation data appears to agree with theirs we note and correct an error in their analysis." @default.
- W2286847110 created "2016-06-24" @default.
- W2286847110 creator A5028069782 @default.
- W2286847110 date "2015-08-03" @default.
- W2286847110 modified "2023-09-27" @default.
- W2286847110 title "Lattice Simulations of Nonperturbative Quantum Field Theories" @default.
- W2286847110 hasPublicationYear "2015" @default.
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