[Paper Review] The Nonintrinsic Sector of Landau Theory

Trey Li|arXiv (Cornell University)|Mar 23, 2026

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TL;DR

The paper argues that externally written microscale fields can survive coarse graining and enter the Landau free-energy functional as spatially prescribed coefficient fields, defining a nonintrinsic sector of Landau theory under a specific scale hierarchy.

ABSTRACT

Landau theory usually treats free-energy coefficients as intrinsic parameters fixed by thermodynamic variables. We show that externally written microscale fields can survive coarse graining and enter the free-energy functional as spatially prescribed coefficient fields. This defines a nonintrinsic sector of Landau theory. The key condition is a hierarchy of correlation, writing, and frustration lengths. We identify ion-patterned FeRh as a plausible realization.

Motivation & Objective

• Motivate and formalize the idea that Landau coefficients can be externally prescribed under a scale hierarchy.
• Define the intrinsic vs nonintrinsic sectors of Landau theory and provide criteria for writability of coefficient fields.

Proposed method

• Derive a coarse-graining framework showing how a written field D(r) maps to an effective coefficient a_eff(r) via a local function A[D(r)].
• Establish a scale hierarchy with xi (correlation length), ell_D (pattern variation scale), and ell_fr (frustration length): xi << ell_D << ell_fr.
• Provide a concrete inequality-based criterion for nonintrinsic writability: xi << ell_D and ell_D << ell_fr.
• Illustrate with a simple local free-energy density f_loc(m,x)=a(x)m^2 + b m^4 and discuss gradient-flow dynamics.
• Discuss realistic material realization and bounds, focusing on FeRh as a candidate platform.

Experimental results

Research questions

• RQ1 Can externally prescribed microscale fields D(r) persist as coefficient fields in the coarse-grained Landau functional?
• RQ2 What scale hierarchy and material mechanisms enable or exclude writable coefficient fields in Landau theory?
• RQ3 Which materials can realize the nonintrinsic sector, and what are the limiting factors?
• RQ4 How do written coefficient fields bias gradient-flow dynamics and domain-wall motion?],
• RQ5 key_findings':['A written field D(r) can survive coarse graining and enter the Landau functional as a coefficient field a_eff(r) when xi << ell_D and D(r) remains inert to long-range reconstruction (ell_D << ell_fr).','The nonintrinsic sector enlarges the accessible family of Landau functionals by allowing externally specified coefficient fields, potentially scaling with system size as an independent writability parameter.
• RQ6 A simple one-dimensional illustration shows how spatial modulation of a(r) can locally bias bistability and domain-wall dynamics via gradients in a(r).
• RQ7 FeRh is identified as a plausible realization due to its short correlation length relative to patterning scales, its tunable AF-FM transition via ion irradiation, and evidence of controllable spatial modulation persisting under operation.
• RQ8 Exclusion mechanisms include large transformation strains, strong dipolar or magnetostatic coupling, mobility of the written field, and strong electronic or structural back-reaction that undermine locality.