### Abstract

We study the homogeneous nearest–neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition—say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature T, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle (Formula presented.); here (Formula presented.) specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to (Formula presented.) by developing new Ising exact solution results—in particular, there is at least one pure state for each (Formula presented.).

Original language | English (US) |
---|---|

Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

DOIs | |

State | Accepted/In press - Nov 13 2017 |

### Fingerprint

### Keywords

- Exact solutions
- Extremal state
- Ising model

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*, 1-16. https://doi.org/10.1007/s10955-017-1918-4

**A Continuum of Pure States in the Ising Model on a Halfplane.** / Abraham, Douglas; Newman, Charles; Shlosman, Senya.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, pp. 1-16. https://doi.org/10.1007/s10955-017-1918-4

}

TY - JOUR

T1 - A Continuum of Pure States in the Ising Model on a Halfplane

AU - Abraham, Douglas

AU - Newman, Charles

AU - Shlosman, Senya

PY - 2017/11/13

Y1 - 2017/11/13

N2 - We study the homogeneous nearest–neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition—say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature T, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle (Formula presented.); here (Formula presented.) specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to (Formula presented.) by developing new Ising exact solution results—in particular, there is at least one pure state for each (Formula presented.).

AB - We study the homogeneous nearest–neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition—say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature T, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle (Formula presented.); here (Formula presented.) specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to (Formula presented.) by developing new Ising exact solution results—in particular, there is at least one pure state for each (Formula presented.).

KW - Exact solutions

KW - Extremal state

KW - Ising model

UR - http://www.scopus.com/inward/record.url?scp=85033580538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033580538&partnerID=8YFLogxK

U2 - 10.1007/s10955-017-1918-4

DO - 10.1007/s10955-017-1918-4

M3 - Article

AN - SCOPUS:85033580538

SP - 1

EP - 16

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -