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Conservative and non-conservative phase-field models are considered for the numerical simulation of lateral phase separation and coarsening in biological membranes. An unfitted finite element method is devised for these models to allow for…

Numerical Analysis · Mathematics 2019-01-08 Vladimir Yushutin , Annalisa Quaini , Sheereen Majd , Maxim Olshanskii

We investigate the spectral radius and operator norm of the Kac-Ward transition matrix for the Ising model on a general planar graph. We then use the obtained results to identify regions in the complex plane where the free energy density…

Mathematical Physics · Physics 2015-05-19 Marcin Lis

In present work, a relation that connects the integrated correlation function of a trapped two-particle system to infinite volume particles scattering phase shift is derived. It has the potential to provide an alternative approach for…

High Energy Physics - Lattice · Physics 2023-09-20 Peng Guo , Vladimir Gasparian

We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation, to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three…

Mathematical Physics · Physics 2015-06-22 P. C. Bollada , C. E. Goodyer , P. K. Jimack , A. M. Mullis , F. W. Yang

Phase transitions in a modified Nishimori model, including the model considered by Kitatani, on a two-dimensional square lattice are investigated using a tensor-network-based sampling scheme. In this model, generating bond configurations is…

Disordered Systems and Neural Networks · Physics 2026-03-20 Takumi Oshima , Yamato Arai , Koji Hukushima

The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 80's by G\"otze and collaborators. The standard derivation of…

Statistical Mechanics · Physics 2012-06-11 Hugo Jacquin , Frédéric Van Wijland

We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase…

Probability · Mathematics 2007-05-23 H. -O. Georgii

The focus of our work is to identify conditions for the presence of an isotropic-nematic phase transition in the context of a generic system with isotropic competing interactions. The comment 0709.4205 criticizes our results by showing that…

Soft Condensed Matter · Physics 2015-05-13 Daniel G. Barci , Daniel A. Stariolo

We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range…

Statistical Mechanics · Physics 2021-10-27 Jules Guioth , Robert L. Jack

A recently developed coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this purpose, an elastic solid modeled by a linear system of…

Numerical Analysis · Mathematics 2024-09-10 Niklas Kolbe , Siegfried Müller

The phase behavior of grain boundaries can have a strong influence on interfacial properties. Little is known about the emergence of grain boundary phases in elemental metal systems and how they transform. Here, we observe the nanoscale…

We investigate the thermodynamic phase transition taking place in the Blume-Capel model in presence of quenched disorder in three dimensions (3D). In particular, performing Exchange Montecarlo simulations, we study the behavior of the order…

Disordered Systems and Neural Networks · Physics 2015-05-19 Matteo Paoluzzi , Luca Leuzzi , Andrea Crisanti

In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…

Numerical Analysis · Mathematics 2021-12-09 Yali Gao , Daozhi Han , Xiaoming He , Ulrich Rüde

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions/contacts between particles in the…

Statistical Mechanics · Physics 2015-06-15 S. -L. -Y. Xu , J. M. Schwarz

Liquid-liquid phase separation plays a major role in the formation and maintenance of various membrane-less subcellular structures in the cytoplasm and nucleus of cells. Biological condensates contain enhanced concentrations of proteins and…

Soft Condensed Matter · Physics 2023-10-03 Paul C Bressloff

The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and…

Strongly Correlated Electrons · Physics 2009-11-10 J. L. Alonso , A. Cruz , L. A. Fernandez , S. Jimenez , V. Martin-Mayor , J. J. Ruiz-Lorenzo , A. Tarancon

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, $\sigma=\pm1/2$, alternated with…

Statistical Mechanics · Physics 2009-03-12 B. Deviren , M. Keskin , O. Canko

We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions (2D). To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction…

Statistical Mechanics · Physics 2011-10-17 Bin Xi , Shijie Hu , Jize Zhao , Gang Su , B. Normand , Xiaoqun Wang

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…

Soft Condensed Matter · Physics 2019-09-11 Piermarco Fonda , Melissa Rinaldin , Daniela J. Kraft , Luca Giomi

We study the phase diagram of the BCSOS model with an extended interaction range using transfer matrix techniques, pertaining to the (100) surface of single component fcc and bcc crystals. The model shows a 2x2 reconstructed phase and a…

Condensed Matter · Physics 2009-10-28 Paul J. M. Bastiaansen , Hubert J. F. Knops