Solving the frustrated spherical model with q-polynomials

被引:11
作者
Cappelli, A
Colomo, F
机构
[1] Ist Nazl Fis Nucl, I-50125 Florence, Italy
[2] Univ Florence, Dipartimento Fis, I-50125 Florence, Italy
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1998年 / 31卷 / 14期
关键词
D O I
10.1088/0305-4470/31/14/004
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We analyse the spherical model with frustration induced by an external gauge field. This has been recently mapped in infinite dimensions onto a problem of q-deformed oscillators, whose real parameter q measures the frustration. We find the analytic solution of this model by suitably representing the q-oscillator algebra with q-Hermite polynomials. We also present a related matrix model which possesses the same diagrammatic expansion in the planar approximation. Its interaction potential is oscillating at infinity with period log(q), and may lead to interesting metastability phenomena beyond the planar approximation. The spherical model is similarly q-periodic, but does not exhibit such phenomena: actually its low-temperature phase is not glassy and depends smoothly on q.
引用
收藏
页码:3141 / 3151
页数:11
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