# Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models

## Abstract

We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A{sub N-1} root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for the zero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models. - Highlights: Black-Right-Pointing-Pointer Partition function of spin chains of Haldane-Shastry type in magnetic field. Black-Right-Pointing-Pointer Equivalence to classical inhomogeneous Ising models. Black-Right-Pointing-Pointer Free energy per site, other thermodynamic quantities in thermodynamic limit. Black-Right-Pointing-Pointer Zero field, zero temperature limits. Black-Right-Pointing-Pointer Thermodynamic equivalence with ensemblemore »

- Authors:

- Instituto de Ciencias Matematicas, Consejo Superior de Investigaciones Cientificas, 28049 Madrid (Spain)
- Departamento de Fisica Teorica II, Universidad Complutense de Madrid, 28040 Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 22157006

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 327; Journal Issue: 11; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; FREE ENERGY; ISING MODEL; MAGNETIC FIELDS; ONE-DIMENSIONAL CALCULATIONS; PARTITION FUNCTIONS; SPIN; TEMPERATURE ZERO K; THERMODYNAMICS; TRANSFER MATRIX METHOD

### Citation Formats

```
Enciso, Alberto, Finkel, Federico, and Gonzalez-Lopez, Artemio, E-mail: artemio@fis.ucm.es.
```*Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models*. United States: N. p., 2012.
Web. doi:10.1016/J.AOP.2012.07.010.

```
Enciso, Alberto, Finkel, Federico, & Gonzalez-Lopez, Artemio, E-mail: artemio@fis.ucm.es.
```*Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models*. United States. doi:10.1016/J.AOP.2012.07.010.

```
Enciso, Alberto, Finkel, Federico, and Gonzalez-Lopez, Artemio, E-mail: artemio@fis.ucm.es. Thu .
"Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models". United States. doi:10.1016/J.AOP.2012.07.010.
```

```
@article{osti_22157006,
```

title = {Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models},

author = {Enciso, Alberto and Finkel, Federico and Gonzalez-Lopez, Artemio, E-mail: artemio@fis.ucm.es},

abstractNote = {We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A{sub N-1} root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for the zero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models. - Highlights: Black-Right-Pointing-Pointer Partition function of spin chains of Haldane-Shastry type in magnetic field. Black-Right-Pointing-Pointer Equivalence to classical inhomogeneous Ising models. Black-Right-Pointing-Pointer Free energy per site, other thermodynamic quantities in thermodynamic limit. Black-Right-Pointing-Pointer Zero field, zero temperature limits. Black-Right-Pointing-Pointer Thermodynamic equivalence with ensemble of classical Ising models.},

doi = {10.1016/J.AOP.2012.07.010},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = 11,

volume = 327,

place = {United States},

year = {2012},

month = {11}

}