Critical behavior of theO(3)nonlinear sigma model with topological term atθ=πfrom numerical simulations

Abstract

We investigate the critical behaviour at θ = π of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of θ, and on scaling transformations that allow a controlled analytic continuation to real values of θ. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2) 1 Wess-ZuminoNovikov-Witten model, for sufficiently small values of the coupling. *

Self-conjugate representation SU(3) chains

“…We can make Monte Carlo simulations for this lattice action for imaginary angles when the topological term is real. [41][42][43] We set v = 1, and changed the values of g for α = −1/2. We used a multigrid update method 13,44 to decrease autocorrelations.…”

Massive Schwinger model at finite θ

“…Much experience has been developed in the last years by our group in this field, both in the elaboration of efficient algorithms to simulate systems with a theta-vacuum term overcoming the severe sign problem [13,14], as well as in the application of these approaches to the computation of the vacuum energy density and topological charge density for several interesting physical systems [15][16][17][18][19]. Our purpose is to take advantage of this experience to apply these approaches to the computation of the θ dependence of the QCD vacuum energy density.…”

Tensor renormalization group analysis ofCP(N−1)model

“…In order to prove this conjecture, Monte Carlo simulations for the O(3) model with the θ term were conducted in various methods. In spite of the presence of the sign problem, the extended cluster algorithm [11][12][13] and the refined analysis [14][15][16] made the calculation feasible. As a result, the second-order phase transition at θ = π was found and it was shown that the observed critical exponents belong to the universality class of the Wess-Zumino-Novikov-Witten (WZNW) model with a topological coupling k = 1 [17][18][19] as expected [20,21].…”