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Energy-States of Particles with Representational Spin
Department of Mathematics, CSU Channel Islands, Camarillo, CA, USA
Department of Physics, CSU Channel Islands, Camarillo, CA, USA
- 1 Department of Mathematics, CSU Channel Islands, Camarillo, CA, USA
- 2 Department of Physics, CSU Channel Islands, Camarillo, CA, USA
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Abstract
In this paper, an algorithm to produce a transition matrix between all states in ideal anti-paramagetic system under the simulated annealing condition that only moves to lower energy states are accepted. The check the accuracy of the transition matrix is confirmed by computer simulation, showing close agreement between model and simulation results.
KeywordsMarkov Chain Monte CarloSimulated AnnealingSpin 1/2 Particles
- Markov. A.A. (1971) Extension of the Limit Theorems of Probability Theory to a Sum of Variables Connected in a chain. Reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, Volume 1: Markov Chains. John Wiley and Sons.
- Curtiss, J.H. (1953) Monte Carlo Methods for the Iteration of Linear Operators. Journal of Mathematics and Physics, 32, 209-232. http://dx.doi.org/10.1002/sapm1953321209
- Kirkpatrick, S., Gelatt Jr., C.D. and Vecchi, M.P. (1983) Optimization by Simulated Annealing. Science, 220, 671680, http://dx.doi.org/10.1126/science.220.4598.671
- Cerny, V. (1985) Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm. Journal of Optimization Theory and Applications, 45, 4151. http://dx.doi.org/10.1007/BF00940812
- DiStasio Jr., R.A., Marcotte, E., Car, R., Stillinger, F.H. and Torquato, S. (2013) Designer Spin Systems via Inverse Statistical Mechanics. Physical Review B, 88, Article ID: 134104. http://dx.doi.org/10.1103/PhysRevB.88.134104
- Grest, G.S., Soukoulis, C.M. and Levin, K. (1986) Cooling-Rate Dependence for the Spin-Glass Ground-State Energy: Implications for Optimization by Simulated Annealing. Physical Review Letters, 56, 1148-1151. http://dx.doi.org/10.1103/PhysRevLett.56.1148