A new algorithm for Monte Carlo simulation of Ising spin systems

Bortz, Alfred B.; Kalos, M. H.; Lebowitz, Joel L.

doi:10.1016/0021-9991(75)90060-1

Cited by 2,183 publications

(1,656 citation statements)

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“…In the AKMC approach, the evolution of the system is modeled as a sequence of vacancy jumps occurring at a rate C ¼ m expðÀE a =k B TÞ, where m is the attempt frequency and E a is the vacancy migration energy. At each jump, the time step is estimated through the residence time algorithm [15].…”

Section: Akmc Algorithmmentioning

confidence: 99%

Stability and mobility of small vacancy–solute complexes in Fe–MnNi and dilute Fe–X alloys: A kinetic Monte Carlo study

Messina

Malerba

Olsson

2015

Nuclear Instruments and Methods in Physics Research Section B:

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a b s t r a c tManganese and nickel solute atoms in irradiated ferritic steels play a major role in the nanostructural evolution of reactor pressure vessels (RPV), as they are responsible for the formation of embrittling nanofeatures even in the absence of copper. The stability and mobility of small vacancy-solute clusters is here studied with an atomistic kinetic Monte Carlo approach based on ab initio calculations, in order to investigate the influence of Mn and Ni on the early life of small radiation-induced vacancy clusters, and to provide the necessary parameters for advanced object kinetic Monte Carlo simulations of the RPV longterm nanostructural evolution. Migration barriers are obtained by direct ab initio calculations or through a binding energy model based on ab initio data. Our results show a clear immobilizing and stabilizing effect on vacancy clusters as the solute content is increased, whereas the only evident difference between the two solute species is a somewhat longer elongation of the cluster mean free path in the presence of a few Mn atoms.

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Section: Akmc Algorithmmentioning

confidence: 99%

Stability and mobility of small vacancy–solute complexes in Fe–MnNi and dilute Fe–X alloys: A kinetic Monte Carlo study

Messina

Malerba

Olsson

2015

Nuclear Instruments and Methods in Physics Research Section B:

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“…However, the usual tacit assumption that is presented: that M commutes with t, is only strictly true in the large volume limit. In a rigorous sense, the continuous-time method is a nonequilibrium Monte Carlo method [19], as we have presented it here, where the noncommutativity of M and t can be realised in the numerical simulation of a finite system.…”

Section: B Continuous-timementioning

confidence: 99%

“…Therefore, as is used explicitly in [15], using this approach it is possible to interchange, t, with, M, and to define the lattice partition via the with respect to a trace operation defined over the length of the Markov chain, rather than with respect to Euclidean-time. A formal definition of the continuous-time properties of the general continuous-time Monte Carlo method is given in [19], and it is explained in detail how, t, and, M, can be interchanged in a general…”

Section: B Continuous-timementioning

confidence: 99%

“…Therefore, because of the more rigorous functional definition of the probabilistic interval that the steps in the Markov chain represent, there is no restriction on the number of steps in the Markov chain, and it is possible to represent the Markov chain by only one step. This is also the rigorous basis of dropping the usual statistical configuration index on lattice partition functions evaluated via the Monte Carlo method, [19]. To be clear, this is not the usual way that the boundary conditions of the continuous-time QMC method in [15] are presented in review articles [20][21].…”

Section: B Continuous-timementioning

confidence: 99%

“…In fact, to write (6), the trace over t = {1, T } has been replaced in (6) by a trace over just one site, M = {1, 2}, through the exchange t ↔ M. To write the lattice partition function in this form we have used the continuous-time properties of the general continuous-time Monte Carlo method defined in [19]. We have noticed, firstly, that both the number of discrete sites in Euclidean-time, T , and the number of discrete steps in the Markov chain, M, are arbitrarily defined for the partition function in (4).…”

Section: B Continuous-timementioning

confidence: 99%

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The partition function zeroes of quantum critical points

Crompton¹

2009

Nuclear Physics B

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The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e h∆τ , and the Euclidean-time lattice spacing ∆τ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as parity. We now present a first numerical analysis for this new zeros approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

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