Bootstrapping MN and Tetragonal CFTs in Three Dimensions (1904.00017v2)
Conformal field theories (CFTs) with MN and tetragonal global symmetry in dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large- expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups and , a second kink is found. In the case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.
Laura Foini, Jorge Kurchan
Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the Eigenstate Thermalization Hypothesis (ETH), we test the hypothesis that the same relation holds in quantum systems that are non-localized, when one considers small energy differences. The relation provides a stringent test of ETH beyond the Gaussian ensemble. We apply it to a disordered spin chain, the SYK model and a Floquet system.
The Role of Pressure in Inverse Design for Assembly (1906.01508v1)
Beth A. Lindquist, Ryan B. Jadrich, Michael P. Howard, Thomas M. Truskett
Isotropic pairwise interactions that promote the self assembly of complex particle morphologies have been discovered by inverse design strategies derived from the molecular coarse-graining literature. While such approaches provide an avenue to reproduce structural correlations, thermodynamic quantities such as the pressure have typically not been considered in self-assembly applications. In this work, we demonstrate that relative entropy optimization can be used to discover potentials that self-assemble into targeted cluster morphologies with a prescribed pressure when the iterative simulations are performed in the isothermal-isobaric ensemble. By tuning the pressure in the optimization, we generate a family of simple pair potentials that all self-assemble the same structure. Selecting an appropriate simulation ensemble to control the thermodynamic properties of interest is a general design strategy that could also be used to discover interaction potentials that self-assemble structures having, for example, a specified chemical potential.
Self-planting: digging holes in rough landscapes (1906.01490v1)
Dhruv Sharma, Jean-Philippe Bouchaud, Marco Tarzia, Francesco Zamponi
Motivated by a potential application in economics, we investigate a simple dynamical scheme to produce planted solutions in optimization problems with continuous variables. We consider the perceptron model as a prototypical model. Starting from random input patterns and perceptron weights, we find a locally optimal assignment of weights by gradient descent; we then remove misclassified patterns (if any), and replace them by new, randomly extracted patterns. This "remove and replace" procedure is iterated until perfect classification is achieved. We call this procedure "self-planting" because the "planted" state is not pre-assigned but results from a co-evolution of weights and patterns. We find an algorithmic phase transition separating a region in which self-planting is efficiently achieved from a region in which it takes exponential time in the system size. We conjecture that this transition might exist in a broad class of similar problems.
Pablo M. Piaggi, Michele Parrinello
From the Ising model and the Lennard-Jones fluid, to water and the iron-carbon system, phase diagrams are an indispensable tool to understand phase equilibria. In spite of the effort of the simulation community the calculation of a large portion of a phase diagram using computer simulation is still today a significant challenge. Here we propose a method to calculate phase diagrams involving liquid and solid phases by the reversible transformation of the liquid and the solid. To this end we introduce an order parameter that breaks the rotational symmetry and we leverage our recently introduced method to sample the multithermal-multibaric ensemble. In this way in a single molecular dynamics simulation we are able to compute the liquid-solid coexistence line for entire regions of the temperature and pressure phase diagram. We apply our approach to the bcc-liquid phase diagram of sodium and the fcc-bcc-liquid phase diagram of aluminum.
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