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We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we…
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
In this work, exact solutions are obtained for a class of generalized gauge-invariant $n$-chain Ising models ($n=1,2,3,4$) with arbitrary multi-spin interactions that are invariant under the local $\mathbb{Z}_2$ gauge group. On a strip…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
The method of counting loops for calculating the partition function of the Ising model on the two dimensional square lattice is extended to lacunary planar lattices, especially scale invariant fractal lattices, the Sierpi\'nsky carpets with…
We study 1/2-BPS Wilson loop operators in maximally supersymmetric Yang-Mills theory on $d$-dimensional spheres. Their vacuum expectation values can be computed at large $N$ through supersymmetric localisation. The holographic duals are…
This paper is our progress report on the project "Ising spectroscopy", devoted to systematic study of the mass spectrum of particles in 2D Ising Field Theory in a magnetic field. Here we address the low-temperature regime, and develop…
We show the three-loop integrability of large N plane-wave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory's Hamiltonian in perturbation theory and taking the…
The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
We consider the Ising model on an $M\times N$ rectangular lattice with an asymmetric self-dual boundary condition, and derive a closed-form expression for its partition function. We show that zeroes of the partition function are given by…
We study the finite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum field theory. Particular attention is focussed on the high…
We investigate perfect matchings and essential spanning forests in planar hyperbolic graphs via circle packings. We prove the existence of nonconstant harmonic Dirichlet functions that vanish in a closed set of the boundary, generalizing a…
For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high…
Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core…
We revisit the one-dimensional ferromagnetic Ising spin-chain with a finite number of spins and periodic boundaries and derive analytically and verify numerically its various stationary and dynamical properties at different temperatures. In…
We study the collapse of two-dimensional polymers, via an O($n$) model on the square lattice that allows for dilution, bending rigidity and short-range monomer attractions. This model contains two candidates for the theta point,…
We study the infinite-dimensional stochastic differential equations (ISDEs) of infinite-particle systems associated with Coulomb random point fields. The stochastic dynamics described by these ISDEs are referred to as Coulomb interacting…
We study the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point.…