相关论文: Finite Size Scaling of Perceptron

We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q>4, separating the…

I present results of simulations of the q=10 and q=20 2-d Potts models in the transition region. The asymptotic finite size behavior sets in only for extremely large lattices. We learn from this simulation that finite size scaling cannot be…

First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations.…

A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…

We investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…

We study numerically the properties of the bayesian perceptron through a gradient descent on the optimal cost function. The theoretical distribution of stabilities is deduced. It predicts that the optimal generalizer lies close to the…

We introduce into the classical perceptron algorithm with margin a mechanism that shrinks the current weight vector as a first step of the update. If the shrinking factor is constant the resulting algorithm may be regarded as a…

We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…

For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of…

The finite-size scaling algorithm based on bulk and surface renormalization of de Oliveira (1992) is tested on q-state Potts models in dimensions D = 2 and 3. Our Monte Carlo data clearly distinguish between first- and second-order phase…

An effective model is introduced to illustrate finite volume effects beyond the usual momentum space constraints. The fluctuations of the chiral order parameter and the net baryon number, as well as their scaling properties, are…

Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1/N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and…

We study the order-disorder transition in two-dimensional incompressible systems of motile particles with alignment interactions through extensive numerical simulations of the incompressible Toner-Tu (ITT) field theory and a detailed…

We analyze large deviations of the time-averaged activity in the one dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large…

On the example of a mean-field Fredrickson-Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics take place at a first-order dynamical phase transition point in the space of time-realizations. We…

Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…

We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…

We consider the finite-size corrections in the Dicke model and determine the scaling exponents at the critical point for several quantities such as the ground state energy or the gap. Therefore, we use the Holstein-Primakoff representation…

The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry…

We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise…