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            <title xml:lang="en">Phase diagram for the generalized Villain model</title>
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            <idno type="halRefHtml">&lt;i&gt;Physical Review B: Condensed Matter (1978-1997)&lt;/i&gt;, 1989, 40 (1), pp.264-272. &lt;a target="_blank" href="https://dx.doi.org/10.1103/PhysRevB.40.264"&gt;&amp;#x27E8;10.1103/PhysRevB.40.264&amp;#x27E9;&lt;/a&gt;</idno>
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                <title xml:lang="en">Phase diagram for the generalized Villain model</title>
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                    <forename type="first">M.</forename>
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              <p>Berge et al. have generalized Villains fully frustrated XY model on a square lattice by multiplying the antiferromagnetic exchange constant by a factor. Using the Monte Carlo method, they find that the specific heat displays both Ising-type and Kosterlitz-Thouless-type phase transitions with TI&lt;TKT, where TI()TKT() as 1, thus implying a multicritical point. Using mean-field theory we find a phase diagram in good qualitative agreement with that found by Berge et al., explicitly producing the tetracritical point at =1, and providing a physical picture for the structure of the phases. The nonferromagnetic, collinear phase for &gt;1 is found to possess antiferromagnetic order. When a magnetic field H is included, the paramagnetic and ferromagnetic phases coalesce to a single collinear phase, and the antiferromagnetic and noncollinear phases coalesce to a single noncollinear phase. The critical surface Hc(T,) separating these phases (which should be characterized by a divergence in the staggered susceptibility) has been determined, again within mean-field theory. A phase-only mode-fluctuation analysis is also presented, yielding results consistent with the mean-field analysis, as well as explicitly revealing the fluctuating modes that become unstable at the transitions; with these modes one can explain the presence (and absence) of susceptibility peaks for the four phase transitions found by Berge et al. For TI&lt;T&lt;TKT, one and only one mode condenses, leading to a standard KT phase transition.</p>
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