Finite-lattice approximations to renormalization groups

@article{citeulike:1439717, abstract = {Accurate calculations of the thermodynamic properties of a system near its critical point are now possible using finite-lattice approximations to renormalization groups. In order to investigate some features of such approximations; we introduce a linear-renormalization-group transformation appropriate to a system of continuous spins like the Gaussian model of Berlin and Kac. We solve the renormalization-group equations for the Gaussian model exactly; and then study in detail a finite-lattice approximation to the renormalization group for the three-dimensional case. The renormalization-group transformation contains a parameter b . The exact transformation has fixed points only for b =2 -5 / 2 . The approximate transformation has fixed points for a range of values of b around 2 -5 / 2 . Eigenvalues of the transformation; which determine critical exponents; depend on the value of b used in the calculation. We study the problem of identifying the correct value of b .}, author = {Bell, Thomas L. and Wilson, Kenneth G. }, citeulike-article-id = {1439717}, doi = {10.1103/PhysRevB.11.3431}, journal = {Physical Review B}, keywords = {physics, statmech, theory}, month = {May}, number = {9}, pages = {3431+}, posted-at = {2008-01-10 01:45:59}, priority = {2}, publisher = {American Physical Society}, title = {Finite-lattice approximations to renormalization groups}, url = {http://dx.doi.org/10.1103/PhysRevB.11.3431}, volume = {11}, year = {1975} }

TY - JOUR ID - citeulike:1439717 L3 - citeulike-article-id:1439717 TI - Finite-lattice approximations to renormalization groups JF - Physical Review B VL - 11 IS - 9 SP - 3431 PB - American Physical Society N2 - Accurate calculations of the thermodynamic properties of a system near its critical point are now possible using finite-lattice approximations to renormalization groups. In order to investigate some features of such approximations; we introduce a linear-renormalization-group transformation appropriate to a system of continuous spins like the Gaussian model of Berlin and Kac. We solve the renormalization-group equations for the Gaussian model exactly; and then study in detail a finite-lattice approximation to the renormalization group for the three-dimensional case. The renormalization-group transformation contains a parameter b . The exact transformation has fixed points only for b =2 -5 / 2 . The approximate transformation has fixed points for a range of values of b around 2 -5 / 2 . Eigenvalues of the transformation; which determine critical exponents; depend on the value of b used in the calculation. We study the problem of identifying the correct value of b . KW - physics KW - statmech KW - theory AU - Bell, Thomas AU - Wilson, Kenneth PY - 1975/05/01/ UR - http://dx.doi.org/10.1103/PhysRevB.11.3431 ER -