Related papers: Correlation inequalities for the uniform 8-vertex …
The Ashkin-Teller model can be formulated as a pair of 2D Ising models, interacting via a four-spin interaction. I consider the case of weak anisotropy (slight a-symmetry between the two Ising layers) and weak coupling. I show that the…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional…
Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of…
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…
We study perturbative unitarity in the scalar sector of the Myers-Pospelov model. The model introduces a preferred four-vector $n$ which breaks Lorentz symmetry and couples to a five-dimension operator. When the preferred four-vector is…
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…
These notes are a short introduction to the Sachdev-Ye-Kitaev model. We discuss: SYK and tensor models as a new class of large N quantum field theories, the near-conformal invariance in the infrared, the computation of correlation…
In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the $\mathcal{N}=1$ supersymmetric generalization of the…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
We address the problem of building theoretical models that help elucidate the function of the visual brain at computational/algorithmic and structural/mechanistic levels. We seek to understand how the receptive fields and topographic maps…
The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally…
This paper presents a method for achieving equilibrium in the ISING Hamiltonian when confronted with unevenly distributed charges on an irregular grid. Employing (Multi-Edge) QC-LDPC codes and the Boltzmann machine, our approach involves…
We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range nearest-neighbor and next-nearest-neighbor couplings which can be…
The correlated probabilistic model introduced and analytically discussed in Hanel et al (2009) is based on a self-dual transformation of the index $q$ which characterizes a current generalization of Boltzmann-Gibbs statistical mechanics,…
We investigate the quantum robustness of the topological order in the toric code on the honeycomb lattice in the presence of a uniform parallel field. For a field in $z$-direction, the low-energy physics is in the flux-free sector and can…
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…
The correlation functions of the Z-invariant Ising model are calculated explicitly using the Vertex Operators language developed by the Kyoto school.
Assuming that the Standard Model of particle physics arises from the $E_8\times E_8$ Heterotic String Theory, we try to solve the discrepancy between the unification scale predicted by this theory ($\approx g_{GUT}\times 5.27\cdot 10^{17}$…
We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent…