Dynamic spin-pair correlations in a Heisenberg chain at infinite temperature based on an extended short-time expansion

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Padé interpolation between the short-time and the long-time behavior of the survival probability, i.e., between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.

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Spin-pair correlations of the classical Heisenberg ferromagnet above and below the critical point: Results of self-consistent Monte Carlo calculations

The European Physical Journal A ◽

10.1007/bf01669446 ◽

1974 ◽

Vol 267 (4) ◽

pp. 261-270 ◽

Cited By ~ 14

Author(s):

Heiner Müller-Krumbhaar

Keyword(s):

Monte Carlo ◽

Critical Point ◽

Heisenberg Ferromagnet ◽

Pair Correlations ◽

Spin Pair ◽

Monte Carlo Calculations ◽

Self Consistent

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rmc-discord: reverse Monte Carlo refinement of diffuse scattering and correlated disorder from single crystals

Journal of Applied Crystallography ◽

10.1107/s1600576721010141 ◽

2021 ◽

Vol 54 (6) ◽

Author(s):

Zachary J. Morgan ◽

Haidong D. Zhou ◽

Bryan C. Chakoumakos ◽

Feng Ye

Keyword(s):

Monte Carlo ◽

Single Crystals ◽

Diffuse Scattering ◽

Electrostatic Interactions ◽

Three Dimensional ◽

Real Space ◽

Scattering Data ◽

Reverse Monte Carlo ◽

Pair Correlations ◽

Spin Pair

A user-friendly program has been developed to analyze diffuse scattering from single crystals with the reverse Monte Carlo method. The approach allows for refinement of correlated disorder from atomistic supercells with magnetic or structural (occupational and/or displacive) disorder. The program is written in Python and optimized for performance and efficiency. Refinements of two user cases obtained with legacy neutron-scattering data demonstrate the effectiveness of the approach and the developed program. It is shown with bixbyite, a naturally occurring magnetic mineral, that the calculated three-dimensional spin-pair correlations are resolved with finer real-space resolution compared with the pair distribution function calculated directly from the reciprocal-space pattern. With the triangular lattice Ba3Co2O6(CO3)0.7, refinements of occupational and displacive disorder are combined to extract the one-dimensional intra-chain correlations of carbonate molecules that move toward neighboring vacant sites to accommodate strain induced by electrostatic interactions. The program is packaged with a graphical user interface and extensible to serve the needs of single-crystal diffractometer instruments that collect diffuse-scattering data.

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