Memory effect and phase transition in a hierarchical trap model for spin glasses

I describe work on 3-d Spin Glasses and the 3-d Ising Model done in collaboration with Michael Creutz at BNL and Jan Lacki at IAS Princeton. We have developed novel techniques to study these systems that make use of parallel architectures. For 3-d spin glasses, our results give strong indication that there is no phase transition in the thermodynamic limit whereas for the Ising model, we are able to extend the weak coupling expansion of the average free energy to 50 excited bonds.

Download Full-text

Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2017392118 ◽

2021 ◽

Vol 118 (11) ◽

pp. e2017392118

Author(s):

Huaping Li ◽

Yuliang Jin ◽

Ying Jiang ◽

Jeff Z. Y. Chen

Keyword(s):

Machine Learning ◽

Phase Transition ◽

Critical Exponents ◽

Spin Glasses ◽

Scaling Laws ◽

Finite Size ◽

Three Dimensions ◽

Aging Effects ◽

Correlation Lengths ◽

Nonequilibrium Phase

Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing down, are ubiquitous in nonequilibrium systems such as supercooled liquids, amorphous solids, active matter, and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case or simply a crossover and even more so to measure the associated critical exponents. Here we show that the simulation results of a hard-sphere glass in three dimensions are consistent with the recent theoretical prediction of a Gardner transition, a continuous nonequilibrium phase transition. Using a hybrid molecular simulation–machine learning approach, we obtain scaling laws for both finite-size and aging effects and determine the critical exponents that traditional methods fail to estimate. Our study provides an approach that is useful to understand the nature of glass transitions and can be generalized to analyze other nonequilibrium phase transitions.

Download Full-text

The effect of social balance on social fragmentation

Journal of The Royal Society Interface ◽

10.1098/rsif.2020.0752 ◽

2020 ◽

Vol 17 (172) ◽

pp. 20200752

Author(s):

Tuan Minh Pham ◽

Imre Kondor ◽

Rudolf Hanel ◽

Stefan Thurner

Keyword(s):

Phase Transition ◽

Social Media ◽

Spin Glasses ◽

Critical Level ◽

Mathematical Structure ◽

Opinion Formation ◽

Social Fragmentation ◽

The Past ◽

Disordered Magnets ◽

Social Balance

With the availability of internet, social media, etc., the interconnectedness of people within most societies has increased tremendously over the past decades. Across the same timespan, an increasing level of fragmentation of society into small isolated groups has been observed. With a simple model of a society, in which the dynamics of individual opinion formation is integrated with social balance, we show that these two phenomena might be tightly related. We identify a critical level of interconnectedness, above which society fragments into sub-communities that are internally cohesive and hostile towards other groups. This critical communication density necessarily exists in the presence of social balance, and arises from the underlying mathematical structure of a phase transition known from the theory of disordered magnets called spin glasses. We discuss the consequences of this phase transition for social fragmentation in society.

Download Full-text