### ?

## Special Purpose Computers for Statistical Physics: achievements and lessons

Cornell University
,
2021.
No. 2107.02406.

In the late 80s and 90s, theoretical physicists of
the Landau Institute for Theoretical Physics designed and
developed several specialized computers for challenging
computational problems in the physics of phase transitions.
These computers did not have a central processing unit. They
optimize algorithms to handle elementary operations on
integers - read, write, compare, and count. The approach
allowed them to achieve recording run times. Computers
performed calculations three orders of magnitude faster than
similar calculations on the world's best supercomputers. The
approach made it possible to obtain fundamentally new results,
some of which have not yet been surpassed in the accuracy of
calculations. The report will present the main ideas for the
development of specialized computers and the scientific results
obtained with their help. The lessons of planning and execution
of long-term complex scientific projects will also be discussed.

Budkov Y., Kalikin N., Kolesnikov A. L., Chemical Communications 2021 Vol. 57 P. 3983-3986

We develop a new quantitative molecular theory of liquid-phase dipolar polymer gels. We model monomer units of the polymer network as a couple of charged sites separated by a fluctuating distance. For the first time, within the random phase approximation, we have obtained an analytical expression for the electrostatic free energy of the dipolar gel. ...

Added: March 26, 2021

Barash L., Marshall J., Weigel M. et al., / Cornell University. Series cond-mat "arxiv.org". 2018. No. 1808.04340.

Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers to quantum computing. Some of the standard approaches suffer from a spurious convergence of the estimates to metastable minima, and these cases are ...

Added: October 17, 2018

Selke W., Shchur L., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 80 P. 042104

The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next-nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin-spin correlations. ...

Added: April 23, 2014

Chertenkov V., Shchur L., Journal of Physics: Conference Series 2021 Vol. 1740 P. 1-5

We formulate the problem of the universality class investigation using machine learning. We chose an example of the universality class of the two-dimensional 4-state Potts model. There are four known models within the universality class – the 4-state Potts model, the Baxter-Wu model, the Ashkin-Teller model, and the Turban model. All four of them together ...

Added: February 19, 2021

Nikerov V. A., М. : Издательско-торговая корпорация «Дашков и Ко», 2012

В учебнике, представляющем собой первую часть краткого современного курса физики для вузов (первая часть - Механика и молекулярная физика, вторая - Электродинамика и волновая оптика, третья - Квантовая физика), изложены основные понятия о законах современной физики, их взаимосвязи и происхождении. В рамках соответствия Государственному образовательному стандарту дано представление о классической механике, специальной теории относительности, колебаниях ...

Added: February 28, 2013

Прудников В. В., Прудников П. В., Маляренко П. Н. et al., Журнал экспериментальной и теоретической физики 2020 Т. 157 № 2 С. 308-326

SImulations of the relaxation of the diluted Ising model from initial states with different magnetization have been done. We measure two-time autocorrelation function and dynamical susceptibility. We found the influence of the percolation threshold dominates the crossover behavior. ...

Added: February 20, 2020

Budkov Y., Kolesnikov A. L., Journal of Statistical Mechanics: Theory and Experiment 2021 Vol. 2021 Article 063213

Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of both distributions. Applying the steepest descent method, we estimate the probability distribution functions (PDFs) of the gyration radius in the limit of a large number ...

Added: June 30, 2021

Smirnov G., Stegailov V., The Journal of Physical Chemistry Letters 2013 Vol. 3 No. 21 P. 3560-3564

Recently, a new phase of hydrogen hydrates has been observed at ∼5−7 kbar and ∼170−250 K. X-ray diffraction patterns do not allow determination of its structure unambiguously. In this work, we perform classical molecular dynamics simulation of hydrogen hydrates and select two possible structures. One of these structures is not a typical clathrate and has ...

Added: March 19, 2014

Budkov Y., Journal of Physics: Condensed Matter 2018 Vol. 30 No. 34 P. 1-9

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small
additive of dipolar particles. We postulate that every dipolar particle is associated with an
arbitrary probability distribution function (PDF) of distance between its charge centers.
Using the standard Hubbard–Stratonovich transformation, we represent the configuration
integral of the system in the functional integral form. We ...

Added: July 31, 2018

Budkov Y., Victorov A., Journal of Molecular Liquids 2021 Vol. 341 Article 117438

Modeling aggregation of ionic micelles in solution is an important task that has been attracting attention for years. The molecular-thermodynamic micellization models describe the electrostatic interactions within the Poisson-Boltzmann theory that does not take into account fluctuations of the surfactant heads in the micelle. In this work we apply the statistical field theory to spherical ...

Added: September 1, 2021

Utesov O., Physical Review B: Condensed Matter and Materials Physics 2022 Vol. 105 Article 054435

A simple mean-field description of frustrated antiferromagnets on hexagonal lattices, aimed to describe the
high-temperature part of the temperature-magnetic field phase diagram, is proposed. It is shown that an interplay
between modulation vector symmetry, Zeeman energy, and magnetodipolar interaction leads to stabilization of
the triple-Q skyrmion lattice in a certain region of the phase diagram. The corresponding analytical ...

Added: March 2, 2022

Yury A. Budkov, Petr E. Brandyshev, Nikolai N. Kalikin, Soft Matter 2023 Vol. 19 P. 3281-3289

Based on the random phase approximation, we develop a molecular theory of self-coacervation in zwitterionic polymer solutions. We show that the interplay between the volume interactions of the monomeric units and electrostatic correlations of charged groups on a polymer backbone can result in liquid-liquid phase separation (self-coacervation). We analyse the behavior of the coacervate phase ...

Added: April 18, 2023

Kolesnikov A. L., Budkov Y., Mollmer J. et al., Journal of Physical Chemistry C 2019 Vol. 123 No. 16 P. 10333-10338

In this manuscript, we study the electrically induced breathing of Metal-Organic Framework (MOF) within a 2D lattice model. The Helmholtz free energy of the MOF in electric eld consists of two parts: the electrostatic energy of the dielectric body in the external electric eld and elastic energy of the framework. The rst contribution is calculated ...

Added: April 1, 2019

Saakian D., Yakushkina T., Hu C., Scientific Reports 2016 Vol. 6

We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase ...

Added: September 16, 2016

O.I. Utesov, Syromyatnikov A. V., Physical Review B: Condensed Matter and Materials Physics 2019 Vol. 100 No. 5 P. 054439

We discuss theoretically phase transitions in frustrated antiferromagnets with biaxial anisotropy or dipolar
forces in magnetic field applied along the easy axis at T = 0. There are well-known sequences of phase
transitions on the field increasing: the conventional spin-flop transition and the flop of the spiral plane at strong
and weak easy-axis anisotropy, respectively. We argue that ...

Added: January 16, 2021

Musaev E., Trachenko K., Bolmatov D., Scientific Reports 2013 Vol. 3

A fundamental task of statistical physics is to start with a microscopic Hamiltonian, predict the system's statistical properties and compare them with observable data. A notable current fundamental challenge is to tell whether and how an interacting Hamiltonian predicts different energy spectra, including solid, liquid and gas phases. Here, we propose a new idea that ...

Added: October 20, 2014

Garkul A., Stegailov V., Scientific Reports 2022 Vol. 12 No. 1 Article 13325

Unlike conventional first-order phase transitions, the kinetics of amorphous-amorphous transitions has been much less studied. The ultrasonic experiments on the transformations between low-density and high-density amorphous ice induced by pressure or heating provided the pressure and temperature dependencies of elastic moduli. In this article, we make an attempt to build a microscopic picture of these ...

Added: August 8, 2022

Слуцкий М. Г., Barash L., Тарасевич Ю. Ю., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2018 Vol. 98 No. 6 P. 062130-1-062130-8

The behavior of the percolation threshold and the jamming coverage for isotropic random sequential adsorption samples has been studied by means of numerical simulations. A parallel algorithm that is very efficient in terms of its speed and memory usage has been developed and applied to the model involving large linear k-mers on a square lattice ...

Added: December 23, 2018

Valba O. V., Tamm M., Nechaev S., Physical Review Letters 2012 Vol. 109 P. 018102

We study the fraction f of nucleotides involved in the formation of a cactuslike secondary structure of random heteropolymer RNA-like molecules. In the low-temperature limit, we study this fraction as a function of the number c of different nucleotide species. We show, that with changing c, the secondary structures of random RNAs undergo a morphological transition:f(c)→1 for c≤ccr as the chain length n goes ...

Added: November 18, 2013

O.I. Utesov, Syromyatnikov A. V., Physical Review B: Condensed Matter and Materials Physics 2018 Vol. 98 No. 18 P. 184406

We discuss theoretically frustrated Heisenberg spiral magnets in magnetic field H. We demonstrate that small
anisotropic spin interactions (single-ion biaxial anisotropy or dipolar forces) select the plane in which spins rotate
(spiral plane) and can lead to the spiral plane flop upon in-plane field increasing. Expressions for the critical
fields Hflop are derived. It is shown that measuring ...

Added: January 16, 2021

Astrakharchik G., Kryuchkov P., Kurbakov I. et al., Crystals 2018 Vol. 8 No. 246 P. 1-26

Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and ...

Added: October 22, 2018

Guskova M.S., Barash L.Yu., Shchur L.N., Computer Physics Communications 2016 Vol. 200 P. 402-405

We present the random number generator (RNG) library RNGAVXLIB, which contains fast AVX realizations of a number of modern random number generators, and also the abilities to jump ahead inside a RNG sequence and to initialize up to 1019 independent random number streams with block splitting method. Fast AVX implementations produce exactly the same output ...

Added: January 31, 2018

Gorsky A., Valba O. V., Journal of Complex Networks 2020 Vol. 8 No. 1 P. cnaa008

In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density p<0.5p<0.5 or as the single cluster at p>0.5p>0.5. We find that there exists ...

Added: August 28, 2020

Ilya D. Fedorov, Vladimir V. Stegailov, ChemPhysChem 2023 Vol. 24 No. 6 Article e202200730

The transition of warm dense fluid hydrogen from an insulator to a conducting state at pressures of about 20–400 GPa and temperatures of 500–5000 K has been the subject of active scientific research over the past few decades. However, various experimental and theoretical methods do not provide consistent results. In this work, we have applied the restricted ...

Added: January 31, 2023