Jacopo Viti

On three-point connectivity in two-dimensional percolation

We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below pc are also given.

Universal amplitude ratios of two-dimensional percolation from field theory

We complete the determination of the universal amplitude ratios of two-dimensional percolation within the two-kink approximation of the form factor approach. For the cluster size ratio, which has for a long time been elusive both theoretically and numerically, we obtain the value 160.2, in good agreement with the lattice estimate 162.5 ± 2 of Jensen and Ziff.

On the theory of quantum quenches in near-critical systems

The theory of quantum quenches in near-critical one-dimensional systems formulated in [J. Phys. A 47 (2014) 402001] yields analytic predictions for the dynamics, unveils a qualitative difference between non-interacting and interacting systems, with undamped oscillations of one-point functions occurring only in the latter case, and explains the presence and role of different time scales. Here we examine additional aspects, determining in particular the relaxation value of one-point functions for small quenches. For a class of quenches we relate this value to the scaling dimensions of the operators. We argue that the

Phase separation and interface structure in two dimensions from field theory

E_8

Universal properties of Ising clusters and droplets near criticality

spectrum of the Ising chain can be more accessible through a quench than at equilibrium, while for a quench of the plane anisotropy in the XYZ chain we obtain that the one-point function of the quench operator switches from damped to undamped oscillations at

Potts q-color field theory and scaling random cluster model

\Delta=1/2

Crossing probability and number of crossing clusters in off-critical percolation

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The density profile of the six vertex model with domain wall boundary conditions

We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly takes into account the topological nature of the elementary excitations. The result known for the Ising model from its lattice solution is recovered as a particular case. In the asymptotic infrared limit the interface behaves as a simple curve characterized by a Gaussian passage probability density. The leading deviation, due to branching, from this behavior is also derived and its coefficient is determined for the Potts model. As a byproduct, for random percolation we obtain the asymptotic density profile of a spanning cluster conditioned to touch only the left half of the boundary.

Phase separation in the six-vertex model with a variety of boundary conditions

Abstract Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use integrable field theory to determine amplitude ratios which characterize the approach to criticality within these two universality classes of percolative critical behavior.

The coprime quantum chain

Abstract We study structural properties of the q -color Potts field theory which, for real values of q , describes the scaling limit of the random cluster model. We show that the number of independent n -point Potts spin correlators coincides with that of independent n -point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the spin fields for generic q is also identified. For the two-dimensional case, we analyze the duality relation between spin and kink field correlators, both for the bulk and boundary cases, obtaining in particular a sum rule for the kink–kink elastic scattering amplitudes.