Microcanonical relation between continuous and discrete spin models

Physical Review Letters

Volumn 106, Issue 5, 2011, Pages

  Casetti, Lapo ^a   Nardini, Cesare ^a   Nerattini, Rachele ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE EXPRESSIONS; CRITICAL ENERGY; CRITICAL ENERGY DENSITY; ENERGY LANDSCAPE; FERRO-MAGNETIC INTERACTIONS; ISING SYSTEMS; KOSTERLITZ-THOULESS TRANSITIONS; LONG RANGE INTERACTIONS; MICROCANONICAL DENSITY; NEAREST-NEIGHBOR INTERACTIONS; NUMERICAL DATA; NUMERICAL RESULTS; SPIN MODELS; STATIONARY POINTS; THREE DIMENSIONS; TWO-DIMENSION; TWO-DIMENSIONAL ISING MODEL; X-Y MODEL;

ISING MODEL;

PHASE TRANSITIONS;

EID: 79551632548     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.106.057208     Document Type: Article

References (38)

1. D.J. Wales, Energy Landscapes (Cambridge University Press, Cambridge, 2004).
2. P.G. Debenedetti and F.H. Stillinger, Nature (London) NATUAS 0028-0836 410, 259 (2001); 10.1038/35065704 (Pubitemid 32218700)
3. F. Sciortino, J. Stat. Mech. 1742-5468 (2005) P05015. 10.1088/1742-5468/2005/05/P05015
4. J.N. Onuchic, Z. Luthey-Schulten, and P.G. Wolynes, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 48, 545 (1997). 10.1146/annurev.physchem.48.1.545
5. F.H. Stillinger and T.A. Weber, Science 225, 983 (1984); SCIEAS 0036-8075 10.1126/science.225.4666.983
6. F.H. Stillinger, Science 267, 1935 (1995). SCIEAS 0036-8075 10.1126/science.267.5206.1935
7. L. Angelani, Phys. Rev. Lett. 85, 5356 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.85.5356 (Pubitemid 32089630)
8. T.S. Grigera, Phys. Rev. Lett. 88, 055502 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.88.055502
9. L. Casetti, M. Pettini, and E.G.D. Cohen, Phys. Rep. 337, 237 (2000). PRPLCM 0370-1573 10.1016/S0370-1573(00)00069-7
10. L. Casetti, M. Pettini, and E.G.D. Cohen, J. Stat. Phys. 111, 1091 (2003). JSTPSB 0022-4715 10.1023/A:1023044014341
11. M. Kastner, Rev. Mod. Phys. 80, 167 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.167
12. M. Pettini, Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics (Springer, New York, 2007).
13. H. Federer, Geometric Measure Theory (Springer, New York, 1969).
14. R.B. Griffiths, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M.S. Green, (Academic Press, London, 1972), Vol. 1.
15. M. Kastner and O. Schnetz, Phys. Rev. Lett. 100, 160601 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.160601 (Pubitemid 351590610)
16. M. Kastner, O. Schnetz, and S. Schreiber, J. Stat. Mech. 1742-5468 (2008) P04025. 10.1088/1742-5468/2008/04/P04025
17. L. Casetti, M. Kastner, and R. Nerattini, J. Stat. Mech. 1742-5468 (2009) P07036. 10.1088/1742-5468/2009/07/P07036
18. L. Casetti and M. Kastner, Physica (Amsterdam) 384A, 318 (2007). PHYADX 0378-4371 10.1016/j.physa.2007.05.043 (Pubitemid 47299288)
19. A. Campa, T. Dauxois, and S. Ruffo, Phys. Rep. 480, 57 (2009). PRPLCM 0370-1573 10.1016/j.physrep.2009.07.001
20. R. Franzosi and M. Pettini, Phys. Rev. Lett. 92, 060601 (2004); PRLTAO 0031-9007 10.1103/PhysRevLett.92.060601
21. R. Franzosi M. Pettini Nucl. Phys. NUPBBO 0550-3213 B782, 219 (2007); 10.1016/j.nuclphysb.2007.04.035
22. R. Franzosi, M. Pettini, and L. Spinelli, Nucl. Phys. NUPBBO 0550-3213 B782, 189 (2007). 10.1016/j.nuclphysb.2007.04.025
23. R. Schilling, Physica (Amsterdam) 216D, 157 (2006); PDNPDT 0167-2789 10.1016/j.physd.2005.12.013 (Pubitemid 44321896)
24. for the 1- d X Y case see M. Kastner and D. Mehta, arXiv:1010.5335.
25. A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002). PRPLCM 0370-1573 10.1016/S0370-1573(02)00219-3
26. A. Campa, A. Giansanti, and D. Moroni, J. Phys. A JPHAC5 0305-4470 36, 6897 (2003). 10.1088/0305-4470/36/25/301
27. R. Gupta and C.F. Baillie, Phys. Rev. B PRBMDO 0163-1829 45, 2883 (1992). 10.1103/PhysRevB.45.2883
28. M. Hasenbusch, J. Phys. A JPHAC5 0305-4470 38, 5869 (2005). 10.1088/0305-4470/38/26/003 (Pubitemid 40901135)
29. A.J.F. de Souza and F.G. Brady Moreira, Phys. Rev. B PRBMDO 0163-1829 48, 9586 (1993). 10.1103/PhysRevB.48.9586
30. A.P. Gottlob and M. Hasenbusch, Physica (Amsterdam) 201A, 593 (1993). PHYADX 0378-4371 10.1016/0378-4371(93)90131-M
31. R.G. Brown and M. Ciftan, Phys. Rev. B PRBMDO 1098-0121 74, 224413 (2006). 10.1103/PhysRevB.74.224413 (Pubitemid 44927307)
32. V.L. Berežinskij, Sov. Phys. JETP 32, 493 (1971); SPHJAR 0038-5646
33. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973). JPSOAW 0022-3719 10.1088/0022-3719/6/7/010
34. X. Leoncini, A.D. Verga, and S. Ruffo, Phys. Rev. E PLEEE8 1063-651X 57, 6377 (1998). 10.1103/PhysRevE.57.6377
35. R. Kenna and A.C. Irving, Nucl. Phys. NUPBBO 0550-3213 B485, 583 (1997). 10.1016/S0550-3213(96)00642-6
36. J. Tobochnik and G.V. Chester, Phys. Rev. B PRBMDO 0163-1829 20, 3761 (1979). 10.1103/PhysRevB.20.3761
37. A. Patrascioiu and E. Seiler, Phys. Rev. B PRBMDO 0163-1829 54, 7177 (1996). 10.1103/PhysRevB.54.7177
38. R. Nerattini, MSc thesis, Università di Firenze, 2010.