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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 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 model
We investigate the behavior of the return amplitude ${cal F}(t)= |langlePsi(0)|Psi(t)rangle|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|Psi(0)r
Fortuin-Kastelyn clusters in the critical $Q$-state Potts model are conformally invariant fractals. We obtain simulation results for the fractal dimension of the complete and external (accessible) hulls for Q=1, 2, 3, and 4, on clusters that wrap aro
The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has b
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the c