### Abstract

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T → 0), the size of the system going to infinity (N →∞ ) while N[1 - tanh(J/k _{B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

Original language | English |
---|---|

Pages (from-to) | 1465-1478 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 |

Issue number | 5 |

DOIs | |

Publication status | Published - Feb 6 2004 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Probability distribution of magnetization in the one-dimensional Ising model : Effects of boundary conditions.** / Antal, T.; Droz, M.; Rácz, Z.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 37, no. 5, pp. 1465-1478. https://doi.org/10.1088/0305-4470/37/5/001

}

TY - JOUR

T1 - Probability distribution of magnetization in the one-dimensional Ising model

T2 - Effects of boundary conditions

AU - Antal, T.

AU - Droz, M.

AU - Rácz, Z.

PY - 2004/2/6

Y1 - 2004/2/6

N2 - Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T → 0), the size of the system going to infinity (N →∞ ) while N[1 - tanh(J/k BT)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

AB - Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T → 0), the size of the system going to infinity (N →∞ ) while N[1 - tanh(J/k BT)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

UR - http://www.scopus.com/inward/record.url?scp=1142265167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1142265167&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/5/001

DO - 10.1088/0305-4470/37/5/001

M3 - Article

AN - SCOPUS:1142265167

VL - 37

SP - 1465

EP - 1478

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 5

ER -