Related papers: Critical spin chains and loop models with $PSU(n)$…
We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with $\mathcal{W}_N$ symmetry in the "irrational" regime, where $c>N-1$ and…
We use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors, which can be assigned different local weights, hence allowing for an explicit Z_2…
Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the…
We solve exactly the general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical…
We study correlation functions of a conserved spin-1 current $J_\mu$ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point…
Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical…
We study the critical properties of scalar field theories in $d+1$ dimensions with $O(N)$ invariant interactions localized on a $d$-dimensional boundary. By a combination of large $N$ and epsilon expansions, we provide evidence for the…
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning…
This thesis studies a pair of symmetry protected topological (SPT) phases which arise when considering one-dimensional quantum spin systems possessing a natural orthogonal group symmetry. Particular attention is given to a family of exactly…
We investigate the critical properties of the three-dimensional (3D) antiferromagnetic RP(N-1}) model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the…
The two-dimensional $O(N)$ nonlinear sigma model (NLSM) is asymptotically free for $N>2$: it exhibits neither a nontrivial fixed point nor spontaneous symmetry-breaking. Here we show that a nontrivial fixed point generically does exist in…
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…
This article reports a measurement of the low-energy excitation spectrum along the critical line for a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields. The measured…
Similarities between fragile glasses and spin glasses (SG) suggest the study of frustrated spin model to understand the complex dynamics of glasses above the glass transition. We consider a frustrated spin model with Ising spins and s-state…
We discuss the relationship between the phase diagram of the Q=0 state Potts model, the arboreal gas model, and the supersphere sigma model S^{0,2} = OSP(1/2) / OSP(0/2). We identify the Potts antiferromagnetic critical point with the…
We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical quantum spin chains with Z_2 x Z_2 on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum…
We study a block mean-field Ising model with $N$ spins split into $s_N$ blocks, with Curie-Weiss interaction within blocks and nearest-neighbor coupling between blocks. While previous models deal with the block magnetization for a fixed…
The so-called regime III of the a_2^{(2)} Izergin-Korepin 19-vertex model has defied understanding for many years. We show in this paper that its continuum limit involves in fact a non compact conformal field theory (the so-called Witten…
The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal…
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple…