Mathematical Sciences: Monodromy Preserving Deformation on  Z2
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The two dimensional Ising model is a mathematical model for                magnetic spins on a lattice which interact by nearest neighbor                  coupling.  There is a vast literature in physics concerning the                 behavior of statistical systems near critical points (phase                     transitions), but there are few models in which it is possible to               verify the conjectured behavior analytically.  The importance of                the Ising model is that it is a notable exception (in two                       dimensions).  There, one has sufficient knowledge of the spin                   correlations to examine some of the more detailed conjectures                   about critical phenomena.  This is of importance for statistical                mechanics, quantum field theory, and the mathematical theories                  upon which the analysis rests.                                                       Professor Palmer is an expert on solvable models, such as the              Ising model, in statistical mechanics.  He is in the forefront                  in exploiting the relevant infinite dimensional group theory and                algebraic geometry that has been so successful in these physical                applications. In prior work he introduced a family of                           lattice models which are mathematical generalizations of the                    Ising model. In the current project he proposes to prove scaling                hypotheses that rely upon prior work on infinite spin groups.                   He is also investigating the possibility of interpreting a certain              invariance in the Ising model as the manifestation of a gauge                   group acting of the determinant bundle associated with a family                 of finite difference operators.  This could clarify the                         appearance of conformal symmetry in solvable lattice models.
{'FirstName': 'John', 'LastName': 'Palmer', 'PI_MID_INIT': 'N', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John N Palmer', 'EmailAddress': 'palmer@math.arizona.edu', 'NSF_ID': '000195453', 'StartDate': '09/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}, {'Code': '126200', 'Text': 'MODERN ANALYSIS'}, {'Code': '126600', 'Text': 'APPLIED MATHEMATICS'}]
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