Related papers: Dynamical Linked Cluster Expansions for Spin Glass…
Graph rules for the linked cluster expansion of the Legendre effective action $\Gamma[\phi]$ are derived and proven in $D\geq 2$ Euclidean dimensions. A key aspect is the weight assigned to articulation vertices which is itself shown to be…
Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system, or has to artificially break certain…
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of…
The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of…
We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behaviour. These models are the quantum analogs of the classical facilitated spin models. Just like their…
The critical behaviour of the dynamical transition of glassy system is controlled by a Replica Symmetric action with n=1 replicas. The most divergent diagrams in the loop expansion correspond at all orders to the solutions of a stochastic…
Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which…
We show that atoms in tilted optical superlattices provide a platform for exploring coupled spin chains of forms that are not present in other systems. In particular, using a period-2 superlattice in 1D, we show that coupled Ising spin…
We describe a controllable and unbiased strong-coupling diagrammatic Monte Carlo technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous strong coupling methods that generally rely on the…
This article considers dynamical entanglement in non-relativistic particle scattering. Three questions are explored: what kinds of entanglement occur in this system, how do global symmetries constrain entanglement, and how do the boundary…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system…
We propose a method based on cluster expansion to study the low activity/high temperature phase of a continuous particle system confined in a finite volume, interacting through a stable and finite range pair potential with negative minimum…
We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact…
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…
We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi…
Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…