Related papers: Geometric properties of the complete-graph Ising m…
A graphical representation based on duplication is developed that is suitable for the study of Ising systems in external fields. Two independent replicas of the Ising system in the same field are treated as a single four-state…
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
Statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops…
We show that a class of spin models, containing the Ashkin-Teller model, admits a generalized random-cluster (GRC) representation. Moreover we show that basic properties of the usual representation, such as FKG inequalities and comparison…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Permanents, hafnians, and loop-hafnians are combinatorial matrix functions closely related to perfect matchings in graphs. These matrix functions arise in the quantum amplitudes of boson configurations in bosonic networks, and the classical…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
Given a graph $G$, we form a random subgraph $G_p$ by including each edge of $G$ independently with probability $p$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite…
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…
The tricritical behavior of the two-dimensional $q$-state Potts model with vacancies for $1\leq q \leq4$ is argued to be encoded in the fractal structure of the geometrical spin clusters of the pure model. The close connection between the…
In this paper, meant as a companion to arXiv:2006.04458, we consider a class of non-integrable $2D$ Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
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…
We study the coevolution of a generalized Glauber dynamics for Ising spins, with tunable threshold, and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of…
A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O($n$) loop model or $n$-component face cubic loop model on the…
Comprehending the connections between the geometric, topological, and dynamical structures of integrable quantum systems with quantum phenomena exploitable in quantum information tasks, such as quantum entanglement, is a major problem in…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…