### Abstract

Original language | English |
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Article number | 505001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 51 |

Issue number | 50 |

DOIs | |

Publication status | Published - 15 Nov 2018 |

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*Journal of Physics A: Mathematical and Theoretical*,

*51*(50), [505001]. https://doi.org/10.1088/1751-8121/aaea02

**Classical phase transitions in a one-dimensional short-range spin model.** / Sarkanych, Petro; Holovatch, Yu; Kenna, Ralph.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 51, no. 50, 505001. https://doi.org/10.1088/1751-8121/aaea02

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TY - JOUR

T1 - Classical phase transitions in a one-dimensional short-range spin model

AU - Sarkanych, Petro

AU - Holovatch, Yu

AU - Kenna, Ralph

PY - 2018/11/15

Y1 - 2018/11/15

N2 - Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states. Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.

AB - Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states. Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.

U2 - 10.1088/1751-8121/aaea02

DO - 10.1088/1751-8121/aaea02

M3 - Article

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 50

M1 - 505001

ER -