## Spin-dynamics simulations of the three-dimensional XY model: structure factor and transport properties, Phys (1999)

Venue: | Rev. B |

Citations: | 2 - 0 self |

### BibTeX

@ARTICLE{Krech99spin-dynamicssimulations,

author = {M. Krech},

title = {Spin-dynamics simulations of the three-dimensional XY model: structure factor and transport properties, Phys},

journal = {Rev. B},

year = {1999},

pages = {3375}

}

### OpenURL

### Abstract

We present extensive Monte-Carlo spin dynamics simulations of the classical XY model in three dimensions on a simple cubic lattice with periodic boundary conditions. A recently developed efficient integration algorithm for the equations of motion is used, which allows a substantial improvement of statistics and large integration times. We find spin wave peaks in a wide range around the critical point and spin diffusion for all temperatures. At the critical point we find evidence for a violation of dynamic scaling in the sense that independent components of the dynamic structure factor S(q,ω) require different dynamic exponents in order to obtain scaling. Below the critical point we investigate the dispersion relation of the spin waves and the linewidths of S(q,ω) and find agreement with mode coupling theory. Apart from strong spin wave peaks we observe additional peaks in S(q,ω) which can be attributed to two-spin wave interactions. The overall lineshapes are also discussed and compared to mode coupling predictions. Finally, we present first results for the transport coefficient D(q,ω) of the out-of-plane magnetization component at the critical point, which is related to the thermal conductivity of 4 He near the superfluid-normal transition.

### Citations

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Statistical Field Theory Addison-Wesley
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Citation Context ...et using REVTEX 1I. INTRODUCTION The theoretical investigation of classical spin systems has played a key role in the understanding of phase transitions, critical behavior, scaling, and universality =-=[1,2]-=-. In particular, the claasical Ising, the XY, and the Heisenberg model are the most relevant spin models in three dimensions. Each of these simple models represents a universality class which, apart f... |

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Citation Context ...et using REVTEX 1I. INTRODUCTION The theoretical investigation of classical spin systems has played a key role in the understanding of phase transitions, critical behavior, scaling, and universality =-=[1,2]-=-. In particular, the claasical Ising, the XY, and the Heisenberg model are the most relevant spin models in three dimensions. Each of these simple models represents a universality class which, apart f... |

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Citation Context ...to their fundamental role in the understanding of the critical dynamics in magnets Heisenberg ferro- and antiferromagnets have been thoroughly studied analytically by mode coupling theories (see Ref. =-=[5]-=- for a general overview) especially in presence of dipolar interactions [6] and numerically by spin dynamics in d = 2 [7] and in d = 3 [8,9] and by methods closely related to molecular dynamics [10]. ... |

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Citation Context ...corrections yield the dominant contribution to the measured effective exponent ωw. For a clarification of this point more information is needed from analytical theories of dynamic finite-size scaling =-=[38]-=- and from simulations [39]. V. SPIN TRANSPORT AND THERMAL CONDUCTIVITY We have already mentioned in the introduction that the transport properties of the XY model near the critical point provide latti... |

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to appear in Computer Simulation Studies in Condensed Matter Physics XII, edited by
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Citation Context ...nant contribution to the measured effective exponent ωw. For a clarification of this point more information is needed from analytical theories of dynamic finite-size scaling [38] and from simulations =-=[39]-=-. V. SPIN TRANSPORT AND THERMAL CONDUCTIVITY We have already mentioned in the introduction that the transport properties of the XY model near the critical point provide lattice analogues of the corres... |

1 |
FIG. 1. Scaling plot for Gl(q)/L 2−η at T = Tc for L = 20 (✸), 40 (+), 60 (✷), and 80 (×) as a function of qL with η = 0.035. Statistical errors of the data are much smaller than the symbol sizes. The dashed line displays the scaling function gl(qL) as gi
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