Related papers: Scaling laws at the critical point
Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The…
We discuss a scaling theory of the lattice response in the vicinity of a finite-temperature critical end point. The thermal expansivity is shown to be more singular than the specific heat such that the Gr\"uneisen ratio diverges as the…
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…
In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned towards its critical value, the response functions change drastically, typically…
We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities.…
Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with various boundary conditions (BC). Using conformal mappings we deduce the exponent $\eta_\sigma(T)$ of the order parameter correlation function…
We study the thermodynamics of an exactly solvable model of a self-interacting partially directed self-avoiding walk (DSAW) in two dimensions, when a force is applied on one end of the chain. The critical force for the unfolding is…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
A class of Aubry-Andr\'e-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point…
We simulate the kinetic Ashkin-Teller model with both ordered and disordered initial states, evolving in contact with a heat-bath at the critical temperature. The power law scaling behaviour for the magnetic order and electric order are…
We derive universal scaling laws for physical observables such as the critical temperature, the chiral condensate, and the pion decay constant as a function of the flavor number near the conformal window of many-flavor QCD in the chiral…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy…
Short-time dynamic scaling behavior of the 3D $\pm J$ Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap…
We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant…
We arrange the loopwise perturbation theory for the critical viscosity exponent $x_{\eta}$, which happens to be very small, as a power series in $x_{\eta}$ itself and argue that the effect of loops beyond two is negligible. We claim that…
On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…
We have extended through beta^{23} the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic…