William Lay

The effective potential, critical point scaling and the renormalization group

The desirability of evaluating the effective potential in field theories near a phase transition ... more The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order parameter in an equilibrium Ising system, when combined with low-order renormalization group results for an ordinary ϕ^4 system, can be used to extract the effective potential. All scaling features are included in the process.

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Dimensional crossover: Mapping from Ginzburg-Landau theory to the two-dimensional Ising model

Analysis of a continuous field theory in two dimensions with use of the density matrix renormalization group

by William Lay and Joseph Rudnick

Physical review letters, Jan 4, 2002

A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a ... more A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the density matrix renormalization group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy.

Analysis of a Continuous Field Theory in Two Dimensions with Use of the Density Matrix Renormalization Group

Physical Review Letters, 2002

A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a ... more A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the density matrix renormalization group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy.

Effective potential, critical point scaling, and the renormalization group

by Joseph Rudnick and William Lay

Physical Review E, 1998

The desirability of evaluating the effective potential in field theories near a phase transition ... more The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different contexts. We show that recent Monte Carlo simulations for the probability distribution of the order parameter in a dimensional equilibrium Ising system, when combined with low-order renormalization group results for a scalar phi^4 system, can be used to extract the effective potential. All scaling features are included in the process. Excellent agreement is obtained. We are also able to reproduce an important universal ratio.

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