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arxiv: 1907.01850 · v1 · pith:GLRJ636Znew · submitted 2019-07-03 · ❄️ cond-mat.mtrl-sci

Dynamic magnetic features of a mixed ferro-ferrimagnetic ternary alloy in the form of AB_pC_(1-p)

Mehmet Bati , Mehmet Erta\c{s} This is my paper

Pith reviewed 2026-05-25 10:18 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords ternary alloydynamic magnetic featuresmean-field approximationGlauber dynamicscritical temperatureconcentration ratioferro-ferrimagnetic
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The pith

In this ternary alloy model the critical temperature depends on the concentration ratio of its components.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models the dynamic magnetic behavior of an AB_p C_{1-p} mixed ferro-ferrimagnetic alloy by applying the mean-field approximation to a Glauber-type stochastic process. It tracks how the Hamiltonian parameters, including the concentration p, shape the time-dependent magnetization and the location of the dynamic phase transition. A reader would care because the model predicts that the temperature at which magnetic order disappears is not fixed but shifts directly with the relative amounts of the B and C ions. The calculation is performed with fixed spin values SA = 1/2, SB = 1 and SC = 3/2. The central numerical result is that the critical temperature changes whenever the concentration ratio p is altered.

Core claim

Within the mean-field treatment of Glauber dynamics the dynamic critical temperature of the AB_p C_{1-p} alloy is always dependent on the concentration ratio p that sets the relative numbers of B and C ions.

What carries the argument

Mean-field approximation based on Glauber stochastic dynamics applied to the ternary-alloy Hamiltonian with spins 1/2, 1 and 3/2

If this is right

  • Changing the concentration ratio p moves the dynamic critical temperature to a new value.
  • The Hamiltonian parameters control both the shape of the dynamic hysteresis loops and the location of the phase boundary.
  • The system remains ferro-ferrimagnetic for any p, but the temperature window of ordered behavior narrows or widens with p.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the dependence holds, synthesis recipes could deliberately adjust p to place the operating temperature of a magnetic device just below the transition.
  • The same mean-field framework could be reused to scan other spin combinations or to add next-nearest-neighbor couplings without changing the code structure.
  • A direct test would be to prepare thin-film samples at several p values and measure their AC susceptibility peaks.

Load-bearing premise

The chosen mean-field plus Glauber dynamics on the fixed spin values correctly reproduces the dynamic critical behavior of the real alloy.

What would settle it

An exact Monte Carlo simulation or a laboratory measurement on a physical AB_p C_{1-p} sample that finds the critical temperature independent of p would falsify the dependence.

Figures

Figures reproduced from arXiv: 1907.01850 by Mehmet Bati, Mehmet Erta\c{s}.

Figure 1
Figure 1. Figure 1: The Hamiltonian can be written as follows: 1 1 , (1)                   Η    A B C A B C i AB j j AC j j i j j j j ij i j S J S J S h(t) S S S ξ ξ ξ ξ where <ij> shows a summation over all pairs of the nearest-neighboring sites of different sublattices and JAB > 0 and JAC < 0 (model the ferro-ferrimagnetic interactions) are the nearest￾neighbor exchange constants. h(t) is the os… view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

Dynamic magnetic features of a mixed ferro-ferrimagnetic ternary alloy in the form of AB$_p$C$_{1-p}$, especially. The effect of Hamiltonian parameters on the dynamic magnetic features of the system are investigated. For this aim, an AB$_p$C$_{1-p}$ ternary alloy system was simulated within the mean-field approximation based on a Glauber type stochastic dynamic and for simplicity, A, B and C ions as SA = 1/2, SB = 1 and SC = 3/2, were chosen respectively. It was found that in our dynamic system the critical temperature was always dependent on the concentration ratio of the ternary alloy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript examines the dynamic magnetic properties of a mixed ferro-ferrimagnetic ternary alloy of the form AB_p C_{1-p} within the mean-field approximation using Glauber-type stochastic dynamics. Spins are fixed at SA = 1/2, SB = 1, SC = 3/2. The central claim is that the critical temperature depends on the concentration ratio p.

Significance. Within the chosen mean-field Glauber framework the reported p-dependence of Tc is expected by construction and adds little beyond the model definition itself. The approach may still serve as a simple illustration of concentration effects in ternary alloys, but the mean-field limitation and absence of comparisons to Monte Carlo or experiment restrict its quantitative relevance for real materials.

major comments (1)
  1. [Abstract] Abstract: the statement that 'the critical temperature was always dependent on the concentration ratio of the ternary alloy' is an algebraic consequence of the mean-field equations. The self-consistent equations for the three sublattice magnetizations contain explicit factors of p and (1-p) multiplying the exchange terms; linearization around m=0 therefore produces a characteristic equation whose roots depend on p by definition, not as an independent dynamic discovery.
minor comments (2)
  1. The abstract provides no quantitative Tc(p) values, no range of p, and no mention of the specific Hamiltonian parameters or anisotropy terms used.
  2. No error analysis, stability checks on the mean-field solutions, or comparison against Monte Carlo results for the same Hamiltonian are presented.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review. We respond to the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that 'the critical temperature was always dependent on the concentration ratio of the ternary alloy' is an algebraic consequence of the mean-field equations. The self-consistent equations for the three sublattice magnetizations contain explicit factors of p and (1-p) multiplying the exchange terms; linearization around m=0 therefore produces a characteristic equation whose roots depend on p by definition, not as an independent dynamic discovery.

    Authors: We agree that the p-dependence of the critical temperature is an algebraic consequence of the mean-field equations, arising directly from the explicit concentration factors p and (1-p) in the exchange terms. The linearization around the disordered state yields this dependence by construction, independent of the specific Glauber dynamics employed. While the manuscript applies stochastic dynamics to examine time-dependent behavior, the reported statement about Tc does not constitute an independent dynamic result. We will revise the abstract to clarify that this dependence follows from the mean-field model definition and to better emphasize the dynamic features under study. revision: yes

Circularity Check

1 steps flagged

Tc(p) dependence is algebraic consequence of model definition

specific steps
  1. self definitional [Abstract]
    "It was found that in our dynamic system the critical temperature was always dependent on the concentration ratio of the ternary alloy."

    The AB_p C_{1-p} Hamiltonian and mean-field Glauber equations contain p and (1-p) multipliers on the interaction terms by definition. Solving the linearized critical-point equation therefore yields Tc(p) as an algebraic identity of the chosen model; the dependence is not discovered but built into the starting equations.

full rationale

The paper's headline result states that critical temperature depends on concentration p. The mean-field equations for the ternary alloy AB_p C_{1-p} are constructed with explicit p and (1-p) factors multiplying the exchange terms between sublattices. Linearization around the disordered state therefore produces a characteristic equation whose roots depend on p by direct algebra. The reported dependence follows immediately from the model setup rather than from any independent computation or external input.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on the standard mean-field decoupling and the Glauber master equation; no new entities are introduced. The Hamiltonian parameters themselves are treated as free inputs whose effect is scanned.

free parameters (2)
  • exchange couplings J_AB, J_AC, J_BC and anisotropy terms
    These are the Hamiltonian parameters whose effect on dynamic features is investigated; their specific values are not derived from first principles.
  • concentration p
    p is varied as an external control parameter; the reported dependence of Tc on p is therefore built into the weighted mean-field equations.
axioms (2)
  • domain assumption Mean-field approximation is sufficient to describe the dynamic critical behavior
    Invoked when the authors state they simulate the system within the mean-field approximation based on Glauber dynamics.
  • domain assumption Glauber stochastic dynamics correctly models the time evolution of the spins
    Explicitly chosen as the stochastic dynamic framework.

pith-pipeline@v0.9.0 · 5645 in / 1346 out tokens · 25939 ms · 2026-05-25T10:18:12.928713+00:00 · methodology

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