Tricriticality in crossed Ising chains
Abstract
We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb12O29 and also, conceptually, as a geometry which is intermediate between one and two dimensions. Here, using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.
- Authors:
-
- Univ. of California, Davis, CA (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1477008
- Alternate Identifier(s):
- OSTI ID: 1398736
- Grant/Contract Number:
- SC0014671
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 4; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Cary, T., Singh, R. R. P., and Scalettar, R. T. Tricriticality in crossed Ising chains. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.96.042108.
Cary, T., Singh, R. R. P., & Scalettar, R. T. Tricriticality in crossed Ising chains. United States. https://doi.org/10.1103/PhysRevE.96.042108
Cary, T., Singh, R. R. P., and Scalettar, R. T. Mon .
"Tricriticality in crossed Ising chains". United States. https://doi.org/10.1103/PhysRevE.96.042108. https://www.osti.gov/servlets/purl/1477008.
@article{osti_1477008,
title = {Tricriticality in crossed Ising chains},
author = {Cary, T. and Singh, R. R. P. and Scalettar, R. T.},
abstractNote = {We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb12O29 and also, conceptually, as a geometry which is intermediate between one and two dimensions. Here, using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.},
doi = {10.1103/PhysRevE.96.042108},
journal = {Physical Review E},
number = 4,
volume = 96,
place = {United States},
year = {Mon Oct 09 00:00:00 EDT 2017},
month = {Mon Oct 09 00:00:00 EDT 2017}
}
Web of Science
Works referenced in this record:
Universal ratio of magnetization moments in two-dimensional Ising models
journal, January 1993
- Kamieniarz, G.; Blote, H. W. J.
- Journal of Physics A: Mathematical and General, Vol. 26, Issue 2
Organometalliclike localization of -derived spins in an inorganic conducting niobium suboxide
journal, May 2015
- Lee, K. -W.; Pickett, W. E.
- Physical Review B, Vol. 91, Issue 19
On the possibility of first-order phase transitions in Ising systems of triplet ions with zero-field splitting
journal, May 1966
- Capel, H. W.
- Physica, Vol. 32, Issue 5
Critical properties of an Ising model with dilute long range interactions
journal, January 1991
- Scalettar, R. T.
- Physica A: Statistical Mechanics and its Applications, Vol. 170, Issue 2
Critical Phenomena on Fractal Lattices
journal, September 1980
- Gefen, Yuval; Mandelbrot, Benoit B.; Aharony, Amnon
- Physical Review Letters, Vol. 45, Issue 11
Finite-size effects at temperature-driven first-order transitions
journal, August 1986
- Challa, Murty S. S.; Landau, D. P.; Binder, K.
- Physical Review B, Vol. 34, Issue 3
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
journal, February 1944
- Onsager, Lars
- Physical Review, Vol. 65, Issue 3-4
Unconventional Bose–Einstein Condensations Beyond the "No-Node" Theorem
journal, January 2009
- Wu, Congjun
- Modern Physics Letters B, Vol. 23, Issue 01
Ising Chain with Competing Interactions
journal, November 1970
- Nagle, John F.
- Physical Review A, Vol. 2, Issue 5
Determining the density of states for classical statistical models by a flat-histogram random walk
journal, August 2002
- Landau, D. P.; Wang, F.
- Computer Physics Communications, Vol. 147, Issue 1-2
Ising Model with a Long-Range Interaction in the Presence of Residual Short-Range Interactions
journal, May 1963
- Baker, George A.
- Physical Review, Vol. 130, Issue 4
Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
journal, October 2001
- Wang, Fugao; Landau, D. P.
- Physical Review E, Vol. 64, Issue 5
Nanometer structural columns and frustration of magnetic ordering in
journal, July 2005
- Andersen, E. N.; Klimczuk, T.; Miller, V. L.
- Physical Review B, Vol. 72, Issue 3
Exact solution of Ising model on a small-world network
journal, August 2004
- Viana Lopes, J.; Pogorelov, Yu. G.; Lopes dos Santos, J. M. B.
- Physical Review E, Vol. 70, Issue 2
Exact Results for Itinerant Ferromagnetism in Multiorbital Systems on Square and Cubic Lattices
journal, May 2014
- Li, Yi; Lieb, Elliott H.; Wu, Congjun
- Physical Review Letters, Vol. 112, Issue 21
Theory of the First-Order Magnetic Phase Change in U
journal, January 1966
- Blume, M.
- Physical Review, Vol. 141, Issue 2
Antiferromagnetism and metallic conductivity in Nb12O29
journal, April 1991
- Cava, R. J.; Batlogg, B.; Krajewski, J. J.
- Nature, Vol. 350, Issue 6319
Critical properties of site- and bond-diluted Ising ferromagnets
journal, January 1979
- Yeomans, J. M.; Stinchcombe, R. B.
- Journal of Physics C: Solid State Physics, Vol. 12, Issue 2
Exotic phases of interacting -band bosons
journal, June 2013
- Hébert, F.; Cai, Zi; Rousseau, V. G.
- Physical Review B, Vol. 87, Issue 22
Atomic matter of nonzero-momentum Bose-Einstein condensation and orbital current order
journal, July 2006
- Liu, W. Vincent; Wu, Congjun
- Physical Review A, Vol. 74, Issue 1
Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution
journal, March 1993
- Vollmayr, Katharina; Reger, Joseph D.; Scheucher, Manfred
- Zeitschrift f�r Physik B Condensed Matter, Vol. 91, Issue 1
Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice
journal, November 2005
- Isacsson, A.; Girvin, S. M.
- Physical Review A, Vol. 72, Issue 5
Small-world phenomena in physics: the Ising model
journal, November 2000
- Gitterman, M.
- Journal of Physics A: Mathematical and General, Vol. 33, Issue 47