Absence of anomalous dimension in vertex models: Semidilute solution of directed polymers.
Absence of anomalous dimension in vertex models: Semidilute solution of directed polymers.
复制标题
顶点模型中不存在异常尺寸：定向聚合物的半稀溶液。
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
Rajasekaran
中科院分区：
文献类型：
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作者：
Bhattacharjee;Rajasekaran
We develop a continuum path-integral approach for the ferroelectric five-vertex model in arbitrary d dimensions by mapping it to a directed polymer problem. A renormalization-group approach with an ensuremath{epsilon}=3-d expansion, 3 being the upper critical dimension, is used to study the polymer solution. The free-energy change due to the interaction of the chains has been computed to O(ensuremath{epsilon}), and the exact expression for the second virial coefficient has been obtained. The fixed point of the problem is found to be exactly 2ensuremath{pi}ensuremath{epsilon}. By use of finite-size-scaling theory and thermodynamics, the exponents for the vertex model are obtained from those of the polymeric system as the specific-heat exponent ensuremath{alpha}=(3-d)/2, and the incommensuration exponent ensuremath{eta}ifmmodearelse extasciimacronfi{}=(d-1)/2. The model is anisotropic with two length-scale exponents ${ensuremath{
u}}_{mathrm{?}}$=1 in one direction and ${ensuremath{
u}}_{mathrm{ensuremath{perp}}}$ =1/2 in the remaining d-1 directions. It is shown that there are no anomalous dimensions so that the exponents we obtain are exact.
We develop a continuum path-integral approach for the ferroelectric five-vertex model in arbitrary d dimensions by mapping it to a directed polymer problem. A renormalization-group approach with an ensuremath{epsilon}=3-d expansion, 3 being the upper critical dimension, is used to study the polymer solution. The free-energy change due to the interaction of the chains has been computed to O(ensuremath{epsilon}), and the exact expression for the second virial coefficient has been obtained. The fixed point of the problem is found to be exactly 2ensuremath{pi}ensuremath{epsilon}. By use of finite-size-scaling theory and thermodynamics, the exponents for the vertex model are obtained from those of the polymeric system as the specific-heat exponent ensuremath{alpha}=(3-d)/2, and the incommensuration exponent ensuremath{eta}ifmmodearelse extasciimacronfi{}=(d-1)/2. The model is anisotropic with two length-scale exponents ${ensuremath{
u}}_{mathrm{?}}$=1 in one direction and ${ensuremath{
u}}_{mathrm{ensuremath{perp}}}$ =1/2 in the remaining d-1 directions. It is shown that there are no anomalous dimensions so that the exponents we obtain are exact.