Monte Carlo Method| Monte Carlo Method |
In General
> s.a. computational physics; integration.
* Idea: A statistical method
used to calculate quantities that are too difficult to compute analytically,
in which one generates random events in a computer; Versions are the random
walk (Metropolis) and the Hamiltonian ones.
@ Texts and reviews:
Jadach phy/99 [guide];
Newman & Barkema 99,
Krauth 06 [in statistical physics];
Binder & Heermann 19;
> s.a. specific areas.
@ General references:
Kosztin et al AJP(96)may [diffusion method for minima];
Binder RPP(97) [in statistical physics];
Doye & Wales PRL(98) [optimization and thermodynamics],
CPC(00)phy/99 [self-adapting simplicial grid];
Landau et al AJP(04)oct [Wang-Landau sampling in statistical mechanics];
Kendall et al 05;
Ambegaokar & Troyer AJP(10)feb [error estimation];
During & Kurchan EPL(10)-a1004 [statistical mechanics of Monte Carlo sampling].
Types of Algorithms
> s.a. markov process; Simulated Annealing.
* Markov Chain Monte Carlo method: Different
random configurations of a system are generated by small variations as in a Markov chain
(for example, a random walk), and are then given a probability of being accepted; Two
versions are the Metropolis algorithm and Hamiltonian Monte Carlo.
* Metropolis algorithm: A version of the MCMC
method which applies to a thermal system, for which the probability of acceptance depends
on the temperature; The algorithm fails in systems on the verge of a phase transition.
@ Markov Chain Monte Carlo method:
Ottosen a1206 [rev];
Alexandru et al PRL(16)-a1605 [real-time dynamics on the lattice using the Schwinger-Keldysh formalism];
Betancourt a1706 [history];
Hanada a1808 [intro];
Joseph book(20)-a1912-ln [in quantum field theories].
@ Metropolis algorithm: Bhanot RPP(88);
Berg PRL(03) [for rugged dynamical variables];
Moussa a1903-conf [quantum];
> s.a. path integrals.
@ Other algorithms: Suwa & Todo PRL(10)-a1007 [without detailed balance];
Jansen et al JPCS(13)-a1211,
CPC(14)-a1302 [quasi-Monte Carlo method, and lattice field theories];
Herdeiro & Doyon PRE(16)-a1605 [method for critical systems in infinite volume];
Cai et al a1811
[inchworm Monte Carlo method, open quantum systems];
Edwards et al AP(19)-a1903 [worldline Monte Carlo];
> s.a. Glauber Dynamics.
@ Quantum Monte Carlo: Suzuki ed-93 [condensed matter];
Rombouts et al PRL(06) [new updating scheme];
Anderson 07;
Pollet et al JCP(07) [optimality];
Temme et al Nat(11)mar-a0911 [sampling from Gibbs distribution];
Destainville et al PRL(10);
Fantoni & Moroni JChemP(14)-a1408 [for quantum Gibbs ensemble];
Zen et al PRB(16)-a1605 [improved accuracy and speed];
Gubernatis et al 16 [pedagogical overview];
Becca & Sorella 17 [for correlated systems];
Hangleiter et al SciAdv(20)-a2001 [easing the sign problem];
Mareschal a2103,
a2103 [history].
Applications > s.a. computational physics
by areas [including statistical mechanics, field theory, gravity, quantum mechanics].
@ For fermions: Corney & Drummond PRL(04)qp,
PRB(06)cm/04;
Assaraf et al JPA(07).
@ Astrophysics and cosmology: Hajian PRD(07)ap/06 [Hamiltonian version, and cosmology];
> s.a. black-hole formation; observational cosmology.
@ Other systems: Janke PhyA(98) [disordered systems];
Talbot et al JPA(03) [exact results for simple harmonic oscillator];
Lahbabi & Legoll JSP(13) [multiscale systems in time];
Pavlovsky et al a1410-conf [path integral for relativistic quantum systems];
Silva Fernandes & Fartaria AJP(15)sep [gas-liquid coexistence].
> Other systems: see Chemical
Potential; composite systems; diffusion;
lattice field theory; Mean-Field Method;
schrödinger equation.
> Online resources: see
Wikipedia page.
main page
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