The tricritical point of tricritical directed percolation is determined based on neural network

TL;DR

This paper presents a neural network approach to accurately identify critical points and phase transition boundaries in the tricritical directed percolation model, effectively handling crossover effects and locating the tricritical point.

Contribution

The study introduces a neural network method trained on Monte Carlo data to determine critical points and the tricritical point in the model, addressing challenges posed by crossover effects.

Findings

Successfully identified the tricritical point at q=0.893

Determined phase transition boundaries and crossover regions

Demonstrated neural network effectiveness in phase transition analysis

Abstract

In recent years, neural networks have increasingly been employed to identify critical points of phase transitions. For the tricritical directed percolation model, its steady-state configurations encompass both first-order and second-order phase transitions. Due to the presence of crossover effects, identifying the critical points of phase transitions becomes challenging. This study utilizes Monte Carlo simulations to obtain steady-state configurations under different probabilities $p$ and $q$, and by calculating the increments in average particle density, we observe first-order transitions, second-order transitions, and regions where both types of transitions interact.These Monte Carlo-generated steady-state configurations are used as input to construct and train a convolutional neural network, from which we determine the critical points $p_{c}$ for different probabilities $q$. Furthermore, by learning the steady-state configurations associated with the superheated point $p=p_u$, we locate the tricritical point at $q_{t}=0.893$. Simultaneously, we employed a three-output CNN model to obtain the phase transition boundaries and the range of the crossover regions. Our method offers a neural network-based approach to capture critical points and distinguish phase transition boundaries, providing a novel solution to this problem.