Using numerical simulations, a vortex is studied in the broken phase of the $(2+1)$-d $O(2)$-symmetric scalar field theory in the vicinity of the Wilson-Fisher fixed point. The vortex is an infraparticle that is surrounded by a cloud of Goldstone bosons. The $L$-dependence of the vortex mass in a finite $C$-periodic volume $L^2$ leads to the determination of the renormalized vortex charge.
We solve analytically the renormalization-group equation for the potential of the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4, in order to look for nonperturbative fixed points that were found numerically in a recent stu
dy. We find new real solutions with singularities in the higher derivatives of the potential at its minimum, and complex solutions with branch cuts along the negative real axis.
We investigate by means of Monte Carlo simulation and Finite-Size Scaling analysis the critical properties of the three dimensional O(5) non linear sigma model and of the antiferromagnetic RP2 model, both of them regularized on a lattice. High accura
cy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same Universality Class, provide that rather non standard identifications are made for the momentum-space propagator of the RP2 model. We have also investigated the phase diagram of the RP2 model extended by a second-neighbor interaction. A rich phase diagram is found, where most phase transitions are first order.
Considering different universality classes of the QCD phase transitions, we perform the Monte Carlo simulations of the 3-dimensional $O(1, 2, 4)$ models at vanishing and non-vanishing external field, respectively. Interesting high cumulants of the or
der parameter and energy from O(1) (Ising) spin model, and the cumulants of the energy from O(2) and O(4) spin models are presented. The critical features of the cumulants are discussed. They are instructive to the high cumulants of the net baryon number in the QCD phase transitions.
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration
c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In the d=2, the chiral spin-glass system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.
Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with the finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the
domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the (2+1)-dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space (perp) and imaginary-time (parallel) sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with Nle 28 spins, we obtained the correlation-length critical indices ( u_perp, u_parallel)=(0.45(10),1.04(27)), and the crossover exponent phi=0.7(2). Our results are comparable to ( u_{perp}, u_{parallel})=(0.482,1.230), and phi=0.688 obtained by Diehl and Shpot for the (d,m)=(3,2) Lifshitz point with the epsilon-expansion method up to O(epsilon^2).
M. Hornung
,Joao C. Pinto Barros
,
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(2021)
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"Mass and Charge of the Quantum Vortex in the $(2+1)$-d $O(2)$ Scalar Field Theory"
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Joao C. Pinto Barros
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