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Vacancy and interstitial lines

In the three-dimensional vortex lattice, vacancies and interstitials are actually line defects. This gives them much greater significance than the usual point defects. As line defects, their chemical potential must be either zero (i.e. they are present in equilibrium) or infinite (i.e. a finite energy per unit length). We therefore expect two distinct types of phases, in which these defects are either bound or unbound.

To define an order parameter to distinguish these phases, let us work in the grand canonical ensemble. Imagine defining ``operators'' tex2html_wrap_inline3596 and tex2html_wrap_inline3598 , which remove or insert, respectively, one end of a vortex line at position tex2html_wrap_inline2764 . Consider the correlation function


This measures the free energy of an interstitial line present for a length z in the field direction. If interstitials are unbound, this free energy is zero, and tex2html_wrap_inline3604 will not decay for large z. On the other hand, if interstitials are bound, we expect exponential decay, where the inverse correlation length gives the free energy per unit length of an interstitial line. That is,


where tex2html_wrap_inline3608 is the defect chemical potential per unit length, and we have defined the constant asymptote of tex2html_wrap_inline3604 as the square of the expectation value tex2html_wrap_inline3612 . One may argue that the restriction to equal x and y in the definition of tex2html_wrap_inline3618 is inessential.

The field b arises in the so-called ``Boson mapping'' for assemblies of vortex lines. From work by M.P.A. Fisher and D.-H. Lee, it is known that b is in fact dual to the original Ginzburg-Landau order parameter tex2html_wrap_inline3288 . The existence of the complex order parameter b is thus related to the U(1) symmetry of the original Ginzburg-Landau theory. We will see that its existence allows for the possibility of additional types of glassy phases.

Leon Balents
Thu May 30 08:21:44 PDT 1996