Spontaneous magnetization in the plane
The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium i...
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| Format: | Journal article |
| Language: | English |
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2001
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| _version_ | 1826266426530332672 |
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| author | Nicholls, G |
| author_facet | Nicholls, G |
| author_sort | Nicholls, G |
| collection | OXFORD |
| description | The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions forms a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions. |
| first_indexed | 2024-03-06T20:38:47Z |
| format | Journal article |
| id | oxford-uuid:3389fb3f-409a-4786-9fec-7030d6e92622 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:38:47Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:3389fb3f-409a-4786-9fec-7030d6e926222022-03-26T13:20:49ZSpontaneous magnetization in the planeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3389fb3f-409a-4786-9fec-7030d6e92622EnglishSymplectic Elements at Oxford2001Nicholls, GThe Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions forms a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions. |
| spellingShingle | Nicholls, G Spontaneous magnetization in the plane |
| title | Spontaneous magnetization in the plane |
| title_full | Spontaneous magnetization in the plane |
| title_fullStr | Spontaneous magnetization in the plane |
| title_full_unstemmed | Spontaneous magnetization in the plane |
| title_short | Spontaneous magnetization in the plane |
| title_sort | spontaneous magnetization in the plane |
| work_keys_str_mv | AT nichollsg spontaneousmagnetizationintheplane |