Related papers: Critical Phenomena with Linked Cluster Expansions …
Linked cluster expansions are generalized from an infinite to a finite volume on a $d$-dimensional hypercubic lattice. They are performed to 20th order in the expansion parameter to investigate the phase structure of scalar $O(N)$ models…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result…
Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline…
Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they…
The coil-globule transition of an isolated polymer has been well established to be a second-order phase transition described by a standard tricritical O(0) field theory. We provide compelling evidence from Monte Carlo simulations in four…
We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
We propose a new criterion to analyse the order of phase transitions within a finite size scaling analysis. It refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behaviour…
Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…
Hysteresis is observed at second order phase transitions. Universal scaling formul\ae{} for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical…
In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends on microscopic…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the…
We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first-order in the presence of quenched disorder (specifically, the ferromagnetic/paramagnetic transition of the site-diluted…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…