xy model sine-gordon

xy model sine-gordon

It has been M. Malard ( ) Faculdade UnB Planaltina, Universidade de Brasilia, 73300-000, Planaltina, Federal District, Brazil e-mail: mmalard@unb.br intensively investigated since then. 0000007778 00000 n 0000013857 00000 n 0000031379 00000 n The sine-Gordon solitons are equivalent to the fermions of the Thirring model, of which the sine-Gordon Hamiltonian is the S-dual [1, 2]; to the magnetic vortices of the XY model [3]; to the kinks and dislocations propagating in crys-talline structures [4, 5]; and to the correlation functions in 0000030214 00000 n 0000008103 00000 n 0000002379 00000 n This is motivated by recent experimental works, which report signi cantly di erent defect core energies than predicted by XY-model. 0000005840 00000 n 0000116512 00000 n ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. 0000040697 00000 n 0000044102 00000 n 0000083030 00000 n 0000013880 00000 n explained in many places; see for instance [4,17 – 19]. Exact predictions for the finite volume energy spectrum of the sine-Gordon model were presented recently. Exact entanglement entropy of the XYZ model and its sine-Gordon limit. 0000014320 00000 n Though Wiegmann realised the irrelevance of ‘higher harmonics’ cos nP+ in the low-temperature XY phase, he still 498 0 obj << /Linearized 1 /O 501 /H [ 2379 869 ] /L 688013 /E 122608 /N 17 /T 677934 >> endobj xref 498 88 0000000016 00000 n The two-dimensional XY model with nearest-neighbor interactions is an example of a two-dimensional system with continuous symmetry that does not have long-range order as required by the Mermin–Wagner theorem.Likewise, there is not a conventional phase transition present that would be associated with symmetry breaking.However, as will be discussed later, the system does show signs … 0000003954 00000 n 0000005184 00000 n 0000002338 00000 n 0000007614 00000 n 0000004327 00000 n 0000100764 00000 n 0000005010 00000 n I. 0000044003 00000 n The two dimensional XY model is examined with Monte Carlo methods. 0000083572 00000 n 0000008927 00000 n 0000004721 00000 n 0000081833 00000 n 0000116630 00000 n 0000015914 00000 n H�b```f`��f`g`��cd@ AV�(���V�v�G���n�5?9���wª �F>"Kx�. Copyright © 2020 Elsevier B.V. or its licensors or contributors. 0000003226 00000 n 0000008269 00000 n 0000007120 00000 n 0000007450 00000 n 0000005279 00000 n 0000008601 00000 n 0000029986 00000 n 0000082868 00000 n 0000006451 00000 n 0000003709 00000 n 0000081811 00000 n 0000006954 00000 n The XY model can be linked to SG theory in two steps: first, the Villain approximation [27]totheXY model preserves the periodicity of the phase variable but approximates the cosine angular dependence with a harmonic one, and can be mapped exactly onto the 2D Coulomb gas [28–30]. 0000031581 00000 n 0000007944 00000 n 0000008765 00000 n 0000012495 00000 n Substituting (27) into (25), we nd that our nal dual theory of the XY model is the sine-Gordon theory! Mapping 2D Cl. In this section, we will go through steps of this mapping. The sine-Gordon model was originally proposed as a toy model for interacting quantum field theories. One thing that is interesting is that the temperature t of. 0000042764 00000 n 0000008441 00000 n %PDF-1.4 %���� By continuing you agree to the use of cookies. J. Phys. One can nd a vast num- ber of works that show analogy between 1D quantum system and 2D classical cases as vortex-unbinding in su- per uids. We will focus on one advantage of performing this mapping; ability to assign correct core energies to topological defects in these systems. 0000041113 00000 n 0000009092 00000 n The SCHA was used in the study of the one-dimensional quantum sine-Gordon problem, where it describes correctly the phase transition of the model. 0000010857 00000 n We will start with low temperature phase of XY-model. 0000011290 00000 n trailer << /Size 586 /Info 496 0 R /Root 499 0 R /Prev 677923 /ID[<10a481cb7342a809dba56318b66c358f>] >> startxref 0 %%EOF 499 0 obj << /Metadata 497 0 R /PageMode /UseOutlines /Outlines 502 0 R /PageLabels << /Nums [ 0 << /S /D /St 182 >> ] >> /Pages 493 0 R /Lang (en) /OpenAction [ 501 0 R /Fit ] /Type /Catalog /Names 500 0 R >> endobj 500 0 obj << /Dests 271 0 R >> endobj 584 0 obj << /S 749 /T 972 /O 1034 /E 1050 /Filter /FlateDecode /Length 585 0 R >> stream 0000082890 00000 n 0000004612 00000 n Then we consider the anisotropic scaling limit of the XYZ chain that yields the (1+1)-dimensional sine-Gordon model. A sine-Gordon model can be used to describe quantum phase transition in 1D systems. 0000097939 00000 n 0000078345 00000 n The renormalization equations are the same as those for the Kosterlitz-Thouless transition of the 2D classical XY model [17–19]. nClassical two dimensional systems (XY model) nTwo dimensional quantum problems: superfluid films or superconducting films nYes but 2+1 (time): needs finite temperature or dissipation to get BKT nAlternative: look for 1d quantum problems:1+1 nYes but here temperature is the ennemy.

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