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Volume 4, Issue 1
Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model

J. Kaupužs, R. V. N. Melnik & J. Rimšāns

Commun. Comput. Phys., 4 (2008), pp. 124-134.

Published online: 2008-04

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  • Abstract

Advanced Monte Carlo simulations of magnetisation and susceptibility in 3D XY model are performed at two different coupling constants β =0.55 and β =0.5, completing our previous simulation results with additional data points and extending the range of the external field to twice as small values as previously reported (h ≥ 0.00015625). The simulated maximal lattices sizes are also increased from L=384 to L=512. Our aim is an improved estimation of the exponent ρ, describing the Goldstone mode singularity M(h) = M(+0)+chρ at h → 0, where M is the magnetisation. The data reveal some unexpected small oscillations. It makes the estimation by many-parameter fits of the magnetisation data unstable, and we are looking for an alternative method. Our best estimate ρ = 0.555(17) is extracted from the analysis of effective exponents determined from local fits of the susceptibility data. This method gives stable and consistent results for both values of β, taking into account the leading as well as the subleading correction to scaling. We report also the values of spontaneous magnetisation.

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@Article{CiCP-4-124, author = {Kaupužs , J.V. N. Melnik , R. and Rimšāns , J.}, title = {Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {1}, pages = {124--134}, abstract = {

Advanced Monte Carlo simulations of magnetisation and susceptibility in 3D XY model are performed at two different coupling constants β =0.55 and β =0.5, completing our previous simulation results with additional data points and extending the range of the external field to twice as small values as previously reported (h ≥ 0.00015625). The simulated maximal lattices sizes are also increased from L=384 to L=512. Our aim is an improved estimation of the exponent ρ, describing the Goldstone mode singularity M(h) = M(+0)+chρ at h → 0, where M is the magnetisation. The data reveal some unexpected small oscillations. It makes the estimation by many-parameter fits of the magnetisation data unstable, and we are looking for an alternative method. Our best estimate ρ = 0.555(17) is extracted from the analysis of effective exponents determined from local fits of the susceptibility data. This method gives stable and consistent results for both values of β, taking into account the leading as well as the subleading correction to scaling. We report also the values of spontaneous magnetisation.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7783.html} }
TY - JOUR T1 - Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model AU - Kaupužs , J. AU - V. N. Melnik , R. AU - Rimšāns , J. JO - Communications in Computational Physics VL - 1 SP - 124 EP - 134 PY - 2008 DA - 2008/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7783.html KW - AB -

Advanced Monte Carlo simulations of magnetisation and susceptibility in 3D XY model are performed at two different coupling constants β =0.55 and β =0.5, completing our previous simulation results with additional data points and extending the range of the external field to twice as small values as previously reported (h ≥ 0.00015625). The simulated maximal lattices sizes are also increased from L=384 to L=512. Our aim is an improved estimation of the exponent ρ, describing the Goldstone mode singularity M(h) = M(+0)+chρ at h → 0, where M is the magnetisation. The data reveal some unexpected small oscillations. It makes the estimation by many-parameter fits of the magnetisation data unstable, and we are looking for an alternative method. Our best estimate ρ = 0.555(17) is extracted from the analysis of effective exponents determined from local fits of the susceptibility data. This method gives stable and consistent results for both values of β, taking into account the leading as well as the subleading correction to scaling. We report also the values of spontaneous magnetisation.

J. Kaupužs, R. V. N. Melnik & J. Rimšāns. (2020). Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model. Communications in Computational Physics. 4 (1). 124-134. doi:
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