Conformal Regge theory at finite boost

The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid even away from Regge limit. The representation extends convergence of the OPE by rewriting it as a double integral over continuous spins and dimensions, and features a novel “Regge block”. We test the formula in the conformal fishnet theory, where exact results involving nontrivial Regge trajectories are available.

Disorder-free spin glass transitions and jamming in exactly solvable mean-field models

We construct and analyze a family of MM-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity c=\alpha Mc=αM and becomes exactly solvable in the limit of large number of components M \to \inftyM→∞. We consider generic pp-body interactions between the vectorial Ising/continuous spins with linear/non-linear potentials. The existence of self-generated randomness is demonstrated by showing that the random energy model is recovered from a MM-component ferromagnetic pp-spin Ising model in M \to \inftyM→∞ and p \to \inftyp→∞ limit. In our systems the quenched disorder, if present, and the self-generated disorder act additively. Our theory provides a unified mean-field theoretical framework for glass transitions of rotational degree of freedoms such as orientation of molecules in glass forming liquids, color angles in continuous coloring of graphs and vector spins of geometrically frustrated magnets. The rotational glass transitions accompany various types of replica symmetry breaking. In the case of repulsive hardcore interactions in the spin space, the criticality of the jamming or SAT/UNSTAT transition becomes the same as that of hardspheres.

ON THE TOPOLOGICAL ORIGIN OF ENTANGLEMENT IN ISING SPIN GLASSES

The origin of entanglement in a class of three-dimensional spin models, at low momenta, is traced to topological reasons. The establishment of the result is facilitated by the gauge principle which, in conjunction with the duality mapping of the spin models, enables us to recast them as lattice Chern–Simons theories. The entanglement measures are expressed in terms of the correlators of Wilson lines, loops, and their generalisations. For continuous spins, these yield the invariants of knots and links. For Ising-like models, they can be expressed in terms of three-manifold invariants obtained from finite group cohomology — the so-called Dijkgraaf–Witten invariants.

THE CONTINUOUS SPIN RANDOM FIELD MODEL: FERROMAGNETIC ORDERING IN d≥3

We investigate the Gibbs-measures of ferromagnetically coupled continuous spins in double-well potentials subjected to a random field (our specific example being the ϕ4 theory), showing ferromagnetic ordering in d≥3 dimensions for weak disorder and large energy barriers. We map the random continuous spin distributions to distributions for an Ising-spin system by means of a single-site coarse-graining method described by local transition kernels. We derive a contour-representation for them with notably positive contour activities and prove their Gibbsianness. This representation is shown to allow for application of the discrete-spin renormalization group developed by Bricmont/Kupiainen implying the result in d≥3.