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Register a new userA multicritical Landau-Potts field theory
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We investigate a perturbatively renormalizable $S_{q}$ invariant model with $N=q-1$ scalar field components below the upper critical dimension $d_c=frac{10}{3}$. Our results hint at the existence of multicritical generalizations of the critical models of spanning random clusters and percolations in three dimensions. We also discuss the role of our multicritical model in a conjecture that involves the separation of first and second order phases in the $(d,q)$ diagram of the Potts model.
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We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry $S_q$ in $d=6-epsilon$ (Landau-Potts field theories) and $d=4-epsilon$ (hypertetrahedral models) up to three loops.We use our results to determine the $epsilon$-expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and forests ($qto0$), and bond percolations ($qto1$). We also explicitly verify several expected degeneracies in the spectrum of relevant operators for natural values of $q$ upon analytic continuation, which are linked to logarithmic corrections of CFT correlators, and use the $epsilon$-expansion to determine the universal coefficients of such logarithms.
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 study. 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 perform a detailed investigation of the scaling Potts field theory using the truncated conformal space approach.
We numerically simulate the time evolution of the Ising field theory after quenches starting from the $E_8$ integrable model using the Truncated Conformal Space Approach. The results are compared with two different analytic predictions based on form factor expansions in the pre-quench and post-quench basis, respectively. Our results clarify the domain of validity of these expansions and suggest directions for further improvement. We show for quenches in the $E_8$ model that the initial state is not of the integrable pair state form. We also construct quench overlap functions and show that their high-energy asymptotics are markedly different from those constructed before in the sinh/sine-Gordon theory, and argue that this is related to properties of the ultraviolet fixed point.
We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge, we show how the problem can be studied analytically from first principles, starting from the degrees of freedom (particle modes) of the bulk field theory. After deriving the passage probability of the interface and the order parameter profile in the regime in which the interface is not bound to the wall, we show how the theory accounts at the fundamental level also for the binding transition and its key parameter.
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