Particles, conformal invariance and criticality in pure and disordered systems

Abstract

The two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first order transitions by disorder.

arXiv commentInvited Colloquium article

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• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Evidences of conformal invariance in 2d rigidity percolation
• Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{R}{\mathrm{P}}^2$ Models in Two Dimensions
• Critical points in coupled Potts models and correlated percolation
• Critical points in the $C{P}^{N-1}$ model
• Critical exponents at the Nishimori point
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Nonuniversality in random criticality
• Exact results for spin glass criticality