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Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the…
At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are…
We investigate the clustering and phase separation of a model of ultrasoft, oppositely charged macroions by a combination of Monte Carlo and Molecular Dynamics simulations. Static and dynamic diagnostics, including the dielectric…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…
We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point…
We analyze the bootstrap approach (a dual optimization method to the variational approach) to one-dimensional spin chains, leveraging semidefinite programming to extract numerical results. We study how correlation functions in the ground…
We study the performances of stochastic heuristic search algorithms on Uniquely Extendible Constraint Satisfaction Problems with random inputs. We show that, for any heuristic preserving the Poissonian nature of the underlying instance, the…
We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster…
We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several…
A key technique for controlling numerical stability in sparse direct solvers is threshold partial pivoting. When selecting a pivot, the entire candidate pivot column below the diagonal must be up-to-date and must be scanned. If 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…
Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…
We study the zero-temperature stochastic Ising model on some connected planar quasi-transitive graphs, which are invariant under rotation and translation. The initial spin configuration is distributed according to a Bernoulli product…
We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence…
The QXORSAT problem is the quantified version of the satisfiability problem XORSAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated with random QXORSAT instances. We give a…
We discuss the quantum annealing of the fully-connected ferromagnetic $ p $-spin model in a dissipative environment at low temperature. This model, in the large $ p $ limit, encodes in its ground state the solution to the Grover's problem…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
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…
Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation/coherence threshold have been recently proposed as efficient analog simulators of 2-local spin…