Two-loop renormalization-group analysis of the Burgers-Kardar-Parisi-Zhang equation.
Two-loop renormalization-group analysis of the Burgers-Kardar-Parisi-Zhang equation.
复制标题
Burgers-Kardar-Parisi-Zhang 方程的二环重整化群分析。
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
U. Tauber
中科院分区：
文献类型：
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作者：
Erwin Frey;U. Tauber
A systematic analysis of the Burgers--Kardar-Parisi-Zhang equation in d+1 dimensions by dynamic renormalization-group theory is described. The fixed points and exponents are calculated to two-loop order. We use the dimensional regularization scheme, carefully keeping the full d dependence originating from the angular parts of the loop integrals. For dimensions less than ${mathit{d}}_{mathit{c}}$=2 we find a strong-coupling fixed point, which diverges at d=2, indicating that there is nonperturbative strong-coupling behavior for all densuremath{ge}2. At d=1 our method yields the identical fixed point as in the one-loop approximation, and the two-loop contributions to the scaling functions are nonsingular. For dg2 dimensions, there is no finite strong-coupling fixed point. In the framework of a 2+ensuremath{epsilon} expansion, we find the dynamic exponent corresponding to the unstable fixed point, which described the nonequilibrium roughening transition, to be z=2+O(${mathrm{ensuremath{epsilon}}}^{3}$), in agreement with a recent scaling argument by Doty and Kosterlitz [Phys. Rev. Lett. 69, 1979 (1992)]. Similarly, our result for the correlation length exponent at the transition is 1/ensuremath{
u}=ensuremath{epsilon}+O(${mathrm{ensuremath{epsilon}}}^{3}$). For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.
A systematic analysis of the Burgers--Kardar-Parisi-Zhang equation in d+1 dimensions by dynamic renormalization-group theory is described. The fixed points and exponents are calculated to two-loop order. We use the dimensional regularization scheme, carefully keeping the full d dependence originating from the angular parts of the loop integrals. For dimensions less than ${mathit{d}}_{mathit{c}}$=2 we find a strong-coupling fixed point, which diverges at d=2, indicating that there is nonperturbative strong-coupling behavior for all densuremath{ge}2. At d=1 our method yields the identical fixed point as in the one-loop approximation, and the two-loop contributions to the scaling functions are nonsingular. For dg2 dimensions, there is no finite strong-coupling fixed point. In the framework of a 2+ensuremath{epsilon} expansion, we find the dynamic exponent corresponding to the unstable fixed point, which described the nonequilibrium roughening transition, to be z=2+O(${mathrm{ensuremath{epsilon}}}^{3}$), in agreement with a recent scaling argument by Doty and Kosterlitz [Phys. Rev. Lett. 69, 1979 (1992)]. Similarly, our result for the correlation length exponent at the transition is 1/ensuremath{
u}=ensuremath{epsilon}+O(${mathrm{ensuremath{epsilon}}}^{3}$). For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.