Related papers: A machine learning approach to the Berezinskii-Kos…
Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian…
Recently, the learning by confusion (LBC) approach has been proposed as a machine learning tool to determine the critical temperature Tc of phase transitions without any prior knowledge of its even approximate value. However, the…
The application of generative modeling to many-body physics offers a promising pathway for analyzing high-dimensional state spaces of spin systems. However, unlike computer vision tasks where visual fidelity suffices, physical systems…
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…
For the spin models with continuous symmetry on regular lattices and finite range of interactions the lower critical dimension is d=2. In two dimensions the classical XY-model displays Berezinskii-Kosterlitz-Thouless transition associated…
We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear…
We employ a novel, unbiased renormalization-group approach to investigate non-equilibrium phase transitions in infinite lattice models. This allows us to address the delicate interplay of fluctuations and ordering tendencies in low…
We show that quasi-one dimensional Bose-Einstein condensate under suitable conditions can exhibit a Berezinskii-Kosterlitz-Thouless phase transition. The role played by quantized vortices in two dimensional case, is played in this case by…
It has been known that encoding Boltzmann weights of a classical spin model in amplitudes of a many-body wave function can provide quantum models whose phase structure is characterized by using classical phase transitions. In particular,…
Equilibrium statistical physics is applied to layered neural networks with differentiable activation functions. A first analysis of off-line learning in soft-committee machines with a finite number (K) of hidden units learning a perfectly…
We develop a thermodynamic theory for machine learning (ML) systems. Similar to physical thermodynamic systems which are characterized by energy and entropy, ML systems possess these characteristics as well. This comparison inspire us to…
We investigate infinite-order phase transitions like the Berezinskii-Kosterlitz-Thouless transition observed in a triangular-lattice three-spin interaction model. Based on a field theoretical description and the…
In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo…
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical…
We develop deep autoregressive networks with multi channels to compute many-body systems with \emph{continuous} spin degrees of freedom directly. As a concrete example, we embed the two-dimensional XY model into the continuous-mixture…
Machine learning has revolutionized many fields of science and technology. Through the $k$-Nearest Neighbors algorithm, we develop a model-independent classifier, where the algorithm can classify phases of a model to which it has never had…
We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of…
We have considered two classical lattice-gas models, consisting of particles that carry multicomponent magnetic momenta, and associated with a two-dimensional square lattices; each site can host one particle at most, thus implicitly…
We study $q$-state clock models of regular and Villain types with $q=5,6$ using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for…
We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can…