相关论文: Reducing Frustration in Spin Systems: Social Balan…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…
We consider a detailed-balance violating dynamics whose stationary state is a prescribed Boltzmann distribution. Such dynamics have been shown to be faster than any equilibrium counterpart. We quantify the gain in convergence speed for a…
We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer…
Parisi demonstrated in 1979 that pairwise interactions exhibit a glass spin phase when there is disorder. While he discovered an equilibrium solution of the Sherrington-Kirkpatrick (SK) spin-glass model and we know it as a continuous phase…
Random $K$-satisfiability ($K$-SAT) is a model system for studying typical-case complexity of combinatorial optimization. Recent theoretical and simulation work revealed that the solution space of a random $K$-SAT formula has very rich…
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…
Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin-glass models provide a natural framework to explore this connection, as their energy…
Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster…
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…
Signed networks with positive and negative interaction are widely observed in the real systems. The negative links would induce frustration, then affect global properties of the system. Based on previous studies, frustration of signed…
We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic…
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
Using exact numerical diagonalization and the conformal field theory approach, we study the effect of magnetic frustrations due to diagonal exchange bonds in a system of two coupled mixed-spin $(1,{1/2})$ Heisenberg chains. It is…
We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction $a$ of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…
The frustrated q-state Potts model is solved exactly on a hierarchical lattice, yielding chaos under rescaling, namely the signature of a spin-glass phase, as previously seen for the Ising (q=2) model. However, the ground-state entropy…
We present a spin-1/2 bilayer model for the quantum order-disorder transition which (i) can be solved by mean-field theory for bulk quantities, (ii) becomes critical at the transition, and (iii) allows to include intralayer frustration. We…
We investigate the use of perturbation theory in finite sized frustrated spin systems by calculating the effect of quantum fluctuations on coherent states derived from the classical ground state. We first calculate the ground and first…