Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914749918216192 |
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| author | Mallick, Olivia Acharyya, Muktish |
| author_facet | Mallick, Olivia Acharyya, Muktish |
| contents | The three dimensional anisotropic XY ferromagnet has been studied by Monte Carlo simulation. The ferro-para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature ($T_c^*$) has been found to decrease as the system gets more and more impure (impurity concentration $p$ increases). In the case of bilinear exchange type of anisotropy ($λ$), the pseudocritical temperature ($T_c^*$) increases linearly with $λ$ for any given concentration of nonmagnetic impurity ($p$). The slope of this linear function has been found to depend on the impurity concentration ($p$). The slope decreases linearly with the impurity concentration ($p$). In the case of the single site anisotropy ($D$), the pseudocritical temperature ($T_c^*$) has been found to decrease linearly with $p$ for fixed $D$. The critical temperature (for a fixed set of parameter values) has been estimated from the temperature variation of fourth order Binder cumulants ($U_L$) for different system sizes ($L$). The critical magnetisation ($M(T_c)$) and the maximum value of the susceptibility ($χ_p$) are calculated for different system sizes ($L$). The critical exponents for the assumed scaling laws, $M(T_c) \sim L^{-{β \over ν}}$ and $χ_p \sim L^{γ \over ν}$, are estimated through the finite size analysis. We have estimated, ${β \over ν}$, equals to $0.48\pm0.05$ and $0.37\pm0.04$ for bilinear exchange and single site anisotropy respectively. We have also estimated, ${γ \over ν}$ equals to $1.78\pm0.05$ and $1.81\pm0.05$ for bilinear exchange and single site anisotropy respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09659 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity Mallick, Olivia Acharyya, Muktish Statistical Mechanics The three dimensional anisotropic XY ferromagnet has been studied by Monte Carlo simulation. The ferro-para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature ($T_c^*$) has been found to decrease as the system gets more and more impure (impurity concentration $p$ increases). In the case of bilinear exchange type of anisotropy ($λ$), the pseudocritical temperature ($T_c^*$) increases linearly with $λ$ for any given concentration of nonmagnetic impurity ($p$). The slope of this linear function has been found to depend on the impurity concentration ($p$). The slope decreases linearly with the impurity concentration ($p$). In the case of the single site anisotropy ($D$), the pseudocritical temperature ($T_c^*$) has been found to decrease linearly with $p$ for fixed $D$. The critical temperature (for a fixed set of parameter values) has been estimated from the temperature variation of fourth order Binder cumulants ($U_L$) for different system sizes ($L$). The critical magnetisation ($M(T_c)$) and the maximum value of the susceptibility ($χ_p$) are calculated for different system sizes ($L$). The critical exponents for the assumed scaling laws, $M(T_c) \sim L^{-{β \over ν}}$ and $χ_p \sim L^{γ \over ν}$, are estimated through the finite size analysis. We have estimated, ${β \over ν}$, equals to $0.48\pm0.05$ and $0.37\pm0.04$ for bilinear exchange and single site anisotropy respectively. We have also estimated, ${γ \over ν}$ equals to $1.78\pm0.05$ and $1.81\pm0.05$ for bilinear exchange and single site anisotropy respectively. |
| title | Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2309.09659 |