dispersion_relation_3d Namespace Reference

Functions
float	epstein_zeta_dispersion (float nu, NDArray[np.float64] k)
NDArray[np.float64]	epstein_zeta_dispersion_tab3d (float nu, NDArray[np.float64] qrange)
None	plot_dispersion_relation (NDArray[np.float64] nurange, List[NDArray[np.float64]] data)
None	main ()

Detailed Description

Quantum spin wave dispersion relation for spins on a 3D square lattice.

This script calculates and plots the dispersion relation of quantum spin waves
on a 3D square lattice (Λ=ℤ³) with power-law long-range interactions. The
dispersion relation ω(k) is computed as a function of k₁ for k₂=k₃=0, using
the Epstein zeta function.

Key features:
1. Models ferromagnetic interactions between spins on a lattice.
2. Demonstrates different scaling behaviors:
   - Typical scaling ω(k) ~ k² for ν ≥ d+2 (green line, ν = 5)
   - Anomalous scaling for d < ν < d+2:
     * Linear dispersion ω(k) ~ k for ν = d+1 (orange line, ν = 4)
     * Square root behavior ω(k) ~ k^(1/2) for ν = 3.5 (blue line)

The dispersion relation is calculated using the Epstein zeta function.

Function Documentation

epstein_zeta_dispersion()

float dispersion_relation_3d.epstein_zeta_dispersion	(	float	nu,
		NDArray[np.float64]	k )

Calculate the Epstein zeta dispersion.

epstein_zeta_dispersion_tab3d()

NDArray[np.float64] dispersion_relation_3d.epstein_zeta_dispersion_tab3d	(	float	nu,
		NDArray[np.float64]	qrange )

Generate 3D dispersion table for a given nu and qrange.

main()

None dispersion_relation_3d.main

(

void

)

Main function to compute data and plot the dispersion relation.

plot_dispersion_relation()

None dispersion_relation_3d.plot_dispersion_relation	(	NDArray[np.float64]	nurange,
		List[NDArray[np.float64]]	data )

Plot the dispersion relation.