Related papers: Phase transitions in soft-committee machines
We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such…
The properties of interfaces in non-equilibrium situations are studied by constructing a density matrix with a space-dependent temperature. The temperature gradient gives rise to new terms in the equation for the order parameter. Surface…
We study the learning dynamics of the soft committee machine (SCM) with Rectified Linear Unit (ReLU) activation using a statistical-mechanics approach within the annealed approximation. The SCM consists of a student network with $N$ input…
Discontinuous quantum phase transitions besides their general interest are clearly relevant to the study of heavy fermions and magnetic transition metal compounds. Recent results show that in many systems belonging to these classes of…
Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries also from noisy and imperfect data and…
The dynamics of the 2D Potts ferromagnet when quenched below the transition temperature is investigated in the case of discontinuous phase transition, which is interesting for understandingthe non equilibrium dynamics of systems with many…
We construct a minimal task that isolates conditional learning in neural networks: a surjective map with K-fold ambiguity, resolved by a selector token z, so H(A | B) = log K while H(A | B, z) = 0. The model learns the marginal P(A | B)…
A quantum phase transition that was recently observed in a high-mobility silicon MOSFET is analyzed in terms of a scaling theory. The most striking characteristic of the transition is a divergence of the thermopower, according to an inverse…
Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the…
Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] level-crossing…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
The machine-learning techniques have shown their capability for studying phase transitions in condensed matter physics. Here, we employ the machine-learning techniques to study the nuclear liquid-gas phase transition. We adopt an…
Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…
Recently, there have been many works on the deep learning of statistical ensembles to determine the critical temperature of a possible phase transition. We analyze the detailed structure of an optimized deep learning machine and prove the…
We study the two-dimensional XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and…
Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
Over the past several years, there have been many studies demonstrating the ability of deep neural networks to identify phase transitions in many physical systems, notably in classical statistical physics systems. One often finds that the…
Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in…
We discuss an aspect of neural networks for the purpose of phase transition detection. To this end, we first train the neural network by feeding Ising/Potts configurations with labels of temperature so that it can predict the temperature of…