Griffiths singularity in quasi-one dimensional restricted $\pm J$ Ising spin glass
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909272144609280 |
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| author | Izadi, Fateme Sepehrinia, Reza |
| author_facet | Izadi, Fateme Sepehrinia, Reza |
| contents | We obtain the exact ground state energy of the quasi-one dimensional restricted $\pm J$ Ising spin glass in a uniform magnetic field using the transfer matrix method. Magnetic field dependence allows us to derive the magnetization as a function of concentration and magnetic field. It turns out that, in the limit of zero field, the magnetization tends to a nonzero value with a singular dependence on the magnetic field. We derive the explicit form of the singularity in thermodynamic quantities such as energy $E\simeq E_0+m_0 h + E_1e^{-h_0/h}$, which is an essential singularity known as Griffiths singularity. We confirm our analytical results using the numerical approach based on iterative equations for energy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_19403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Griffiths singularity in quasi-one dimensional restricted $\pm J$ Ising spin glass Izadi, Fateme Sepehrinia, Reza Disordered Systems and Neural Networks Statistical Mechanics We obtain the exact ground state energy of the quasi-one dimensional restricted $\pm J$ Ising spin glass in a uniform magnetic field using the transfer matrix method. Magnetic field dependence allows us to derive the magnetization as a function of concentration and magnetic field. It turns out that, in the limit of zero field, the magnetization tends to a nonzero value with a singular dependence on the magnetic field. We derive the explicit form of the singularity in thermodynamic quantities such as energy $E\simeq E_0+m_0 h + E_1e^{-h_0/h}$, which is an essential singularity known as Griffiths singularity. We confirm our analytical results using the numerical approach based on iterative equations for energy. |
| title | Griffiths singularity in quasi-one dimensional restricted $\pm J$ Ising spin glass |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2407.19403 |