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Weicheng Fu

Publications and source records attributed to Weicheng Fu.

20 records · Page 2Linked to original sources

A New Strategy in Applying the Learning Machine to Study Phase Transitions

In this Letter, we present a new strategy for applying the learning machine to study phase transitions. We train the learning machine with samples only obtained at a non-critical parameter point, aiming to establish intrinsic correlations between the learning machine and the target system. Then, we find that the accuracy of the learning machine, which is the most important performance index in conventional learning machines, is no longer a key goal of the training in our approach. Instead, relatively low accuracy of identifying unlabeled data category can help to determine the critical point with greater precision, manifesting the singularity around the critical point. It thus provides a robust tool to study the phase transition. The classical ferromagnetic and percolation phase transitions are employed as illustrative examples.

cond-mat.stat-mech↗

Universality of Energy Equipartition in One-dimensional Lattices

We show that a general one-dimensional (1D) lattice with nonlinear inter-particle interactions can always be thermalized for arbitrarily small nonlinearity in the thermodynamic limit, thus proving equipartition hypothesis in statistical physics for an important class of systems. Particularly, we find that in the lattices of interaction potential $V(x)=x^2/2+λx^n/n$ with $n\geq4$, there is \textit{a universal scaling law} for the thermalization time $T^{eq}$, i.e., $T^{eq}\proptoλ^{-2}ε^{-(n-2)}$, where $ε$ is the energy density. Numerical simulations confirm that it is accurate for an even $n$. A slight correction is needed for an odd $n$, which is due to the Chirikov overlap occurring in the weakly nonlinear regime between extra vibration modes excited by the asymmetry of potential. Based on this scaling law, as well as previous prediction for the case of $n=3$, a universal formula for the thermalization time for a 1D lattice with a general interaction potential is obtained.

cond-mat.stat-mech↗