**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30169

##### Exact Solution of the Ising Model on the 15 X 15 Square Lattice with Free Boundary Conditions

**Authors:**
Seung-Yeon Kim

**Abstract:**

**Keywords:**
Phase transition,
Ising magnet,
Square lattice,
Freeboundary conditions,
Exact solution.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1329366

**References:**

[1] C. Domb, The Critical Point, Taylor and Francis, London, 1996.

[2] L. Onsager, "Crystal statistics. I. A two-dimensional model with an order-disorder transition", Physical Review, 65 (1944) 117-149.

[3] B. Kaufman, "Crystal statistics. II. Partition function evaluated by spinor analysis", Physical Review, 76 (1949) 1232-1243.

[4] A. E. Ferdinand and M. E. Fisher, "Bounded and inhomogeneous Ising models. I. Specific-heat anomaly of a finite lattice", Physical Review, 185 (1969) 832-846.

[5] G. Bhanot, "A numerical method to compute exactly the partition function with application to theories in two dimensions", Journal of Statistical Physics, 60 (1990) 55-75.

[6] B. Stosic, S. Milosevic, and M. E. Stanley, "Exact results for the twodimensional Ising model in a magnetic field: Tests of finite-size scaling theory", Physical Review B, 41 (1990) 11466-11478.

[7] L. Stodolsky and J. Wosiek, "Exact density of states and its critical behavior", Nuclear Physics B, 413 (1994) 813-826.

[8] S.-Y. Kim, "Yang-Lee zeros of the antiferromagnetic Ising model", Physical Review Letters, 93 (2004) 130604:1-4.

[9] S.-Y. Kim, "Density of Yang-Lee zeros and Yang-Lee edge singularity for the antiferromagnetic Ising model", Nuclear Physics B, 705 (2005) 504-520.

[10] S.-Y. Kim, "Fisher zeros of the Ising antiferromagnet in an arbitrary nonzero magnetic field plane", Physical Review E, 71 (2005) 017102:1- 4.

[11] R. J. Creswick, "Transfer matrix for the restricted canonical and microcanonical ensembles", Physical Review E, 52 (1995) R5735-R5738.

[12] R. J. Creswick and S.-Y. Kim, "Finite-size scaling of the density of zeros of the partition function in first- and second-order phase transitions", Physical Review E, 56 (1997) 2418-2422.

[13] S.-Y. Kim and R. J. Creswick, "Yang-Lee zeros of the Q-state Potts model in the complex magnetic field plane", Physical Review Letters, 81 (1998) 2000-2003.

[14] S.-Y. Kim and R. J. Creswick, "Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field", Physical Review E, 58 (1998) 7006-7012.

[15] R. J. Creswick and S.-Y. Kim, "Microcanonical transfer matrix study of the Q-state Potts model", Computer Physics Communications, 121 (1999) 26-29.

[16] S.-Y. Kim and R. J. Creswick, "Exact results for the zeros of the partition function of the Potts model on finite lattices", Physica A, 281 (2000) 252-261.

[17] S.-Y. Kim and R. J. Creswick, "Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q", Physical Review E, 63 (2001) 066107:1-12.

[18] S.-Y. Kim, "Partition function zeros of the Q-state Potts model on the simple-cubic lattice", Nuclear Physics B, 637 (2002) 409-426.

[19] S.-Y. Kim, "Density of the Fisher zeros for the three-state and four-state Potts models", Physical Review E, 70 (2004) 016110:1-5.

[20] S.-Y. Kim, "Density of Yang-Lee zeros for the Ising ferromagnet", Physical Review E, 74 (2006) 011119:1-7.

[21] S.-Y. Kim, "Honeycomb-lattice antiferromagnetic Ising model in a magnetic field", Physics Letters A, 358 (2006) 245-250.

[22] J. L. Monroe and S.-Y. Kim, "Phase diagram and critical exponent for the nearest-neighbor and next-nearest-neighbor interaction Ising model", Physical Review E, 76 (2007) 021123:1-5.

[23] C.-O. Hwang, S.-Y. Kim, D. Kang, and J. M. Kim, "Ising antiferromagnets in a nonzero uniform magnetic field", Journal of Statistical Mechanics, 7 (2007) L05001:1-8.

[24] S.-Y. Kim, C.-O. Hwang, and J. M. Kim, "Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field", Nuclear Physics B, 805 (2008) 441-450.

[25] S.-Y. Kim, "Ground-state entropy of the square-lattice Q-state Potts antiferromagnet", Journal of the Korean Physical Society, 52 (2008) 551-556.

[26] S.-Y. Kim, "Specific heat of the square-lattice Ising antiferromagnet in a magnetic field", Journal of Physical Studies, 13 (2009) 4006:1-3.

[27] S.-Y. Kim, "Partition function zeros of the square-lattice Ising model with nearest- and next-nearest-neighbor interactions", Physical Review E, 81 (2010) 031120:1-7.

[28] S.-Y. Kim, "Partition function zeros of the honeycomb-lattice Ising antiferromagnet in the complex magnetic-field plane", Physical Review E, 82 (2010) 041107:1-7.

[29] C.-O. Hwang and S.-Y. Kim, "Yang-Lee zeros of triangular Ising antiferromagnets", Physica A, 389 (2010) 5650-5654.

[30] R. Bulirsch and J. Stoer, "Fehlerabschâ”¬Â¿atzungen und extrapolation mit rationalen funktionen bei verfahren vom Richardson-typus", Numerische Mathematik, 6 (1964) 413-427; "Numerical treatment of ordinary differential equations by extrapolation methods", Numerische Mathematik, 8 (1966) 1-13.