Critical behavior of two tensor models in correlated random fields

Bosiljka Tadić, R. Pirc

We study the critical behavior of the q-state Potts model in the presence of quenched random fields, which locally prefer ordering of any one of the q states, and are long-range correlated such that [H(0)H(R${)]}_{\mathrm{av}\mathrm{\ensuremath{\sim}}{R}^{\mathrm{\ensuremath{-}}(d\mathrm{\ensuremath{-}}\ensuremath{\theta})}}$. We find a stable critical behavior controlled by a new random fixed point, and obtain a set of critical exponents within the \ensuremath{\epsilon}\ifmmode \tilde{}\else \~{}\fi{} expansion (\ensuremath{\epsilon}\ifmmode \tilde{}\else \~{}\fi{}=8+\ensuremath{\theta}-d), which cannot be related to those of a pure Potts model of lower dimensionality.

L.L. Gonçalves

Maksimilian Usoltcev, Carolin Wille, Jens Eisert +1 more

Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks with spatially fluctuating parameters. As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions, both in flat geometry and on a hyperbolic disk, where curvature reshapes their long-distance structure. We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term, placing random matchgate networks in direct correspondence with the thermal quantum Hall problem. The resulting phase structure includes localized phases, quantum Hall criticality, and a robust thermal metal with diffusive correlations and spontaneous replica-symmetry breaking. Weak non-Gaussian deformations reduce the symmetry to discrete permutations, generate a mass for the Goldstone modes, and suppress long-range correlations. In this way, typicality offers a route from ensembles of discrete tensor networks to continuum quantum field theories.

Dimo I. Uzunov, E. R. Kokutcheva, YONKO T. MILLEV

Jacques Villain, Thomas Nattermann, Moshe Schwartz

Gilles Tarjus, Ivan Balog, Matthieu Tissier

We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is based on a theoretical description of the whole (d,N) domain of the d-dimensional random-field O(N) model and points to the role of rare events that are overlooked by the proposed derivations of two-exponent scaling. Quite strikingly, however, the numerical estimates of the critical exponents of the random field Ising model are extremely close to the predictions of the two-exponent scaling, so that the issue cannot be decided on the basis of numerical simulations.