Complex Langevin Simulation

Okano, Keisuke; Schülke, L.; Zheng, Bo

doi:10.1143/ptps.111.313

Cited by 24 publications

(24 citation statements)

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“…the stochastically quantized field theory where a fictitious dynamic process is introduced and the conventional field theory is approached in the equilibrium [24,25]. Detailed investigations have been performed, especially for gauge theory and complex systems [26,27]. However, up to now all these studies are only concentrated to the long-time behaviour of the dynamic process and its equilibrium.…”

Section: Discussionmentioning

confidence: 99%

Universality and scaling in short-time critical dynamics

et al. 1997

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Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the magnetization is observed. The new dynamic critical exponent θ as well as the exponents z and 2β/ν are determined from the power law behaviour of the magnetization, auto-correlation and the second moment. Furthermore the calculation has been carried out with both Heat-bath and Metropolis algorithms. All the results are consistent and therefore universality and scaling are confirmed.

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Section: Discussionmentioning

confidence: 99%

Universality and scaling in short-time critical dynamics

et al. 1997

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“…For sufficiently well behaved distributions ρ on C n the action of K can be simply expressed as [15,33] P(x) = d n y e −i y·∇ x ρ(x, y) ≡ d n y ρ(x − iy, y).…”

Section: )mentioning

confidence: 99%

Positive representations of complex distributions on groups

Salcedo¹

2018

J. Phys. A: Math. Theor.

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A normalizable complex distribution P(x) on a manifold M can be regarded as a complex weight, thereby allowing to define expectation values of observables A(x) defined on M . Straightforward importance sampling, x ∼ P, is not available for non positive P, leading to the well-known sign (or phase) problem. A positive representation ρ(z) of P(x) is any normalizable positive distribution on the complexified manifold M c , such that, A(x) P = A(z) ρ for a dense set of observables, where A(z) stands for the analytically continued function on M c . Such representations allow to carry out Monte Carlo calculations to obtain estimates of A(x) P , through the sampling z ∼ ρ. In the present work we tackle the problem of constructing positive representations for complex weights defined on manifolds of compact Lie groups, both abelian and non abelian, as required in lattice gauge field theories. Since the variance of the estimates increase for broad representations, special attention is put on the question of localization of the support of the representations.

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“…[13,14] as the essential prerequisite for a correct CLE process. Some of those modifications, like kernels, were known already in the 1980s [25][26][27], others such as variable transformations, were encountered just recently. In fact the reduction to the Cartan subgroup discussed in the previous section falls into this general category.…”

Section: Stabilization Via Generalizations Of the Clementioning

confidence: 99%

“…The CLE with a kernel can be written aṡ 17) with z = x + iy and a holomorphic function H (see refs. [25][26][27], where H 2 is called the kernel). Separating real and imaginary parts, Eq.…”

Section: S(u) ≡ S(x(u)) (42)mentioning

confidence: 99%

“…A way of modifying the CL process that was discussed already in the 1980s is the introduction of a so-called kernel [25][26][27]. It is nonneutral in the sense that it does not preserve the Langevin evolution of holomorphic observables (but is supposed to preserve the long-time averages of holomorphic observables).…”

Section: A3 Nonneutral Modifications Of the Cle: Holomorphic (Matrixmentioning

confidence: 99%

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Stability of complex Langevin dynamics in effective models

Aarts

James

Pawlowski

et al. 2013

J. High Energ. Phys.

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Abstract:The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the threedimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.

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Complex Langevin Simulation

Cited by 24 publications

References 0 publications

Universality and scaling in short-time critical dynamics

Universality and scaling in short-time critical dynamics

Positive representations of complex distributions on groups

Stability of complex Langevin dynamics in effective models

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