Questions tagged [disorder]

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Why does the variational approach become a lower bound as the number of replicas approach zero

Consider solving a disordered system with Hamiltonian $H[h(x)]$ where $h(x)$ denotes the disorder parameter/random variable at lattice site $x$ (e.g., possibly of independent Gaussian distributions $\...
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Do annealed energies underestimate quenched energies?

In the physics of disordered systems, there are two ways to treat the disorder: Quenched disorder, in which the disordered variables are considered to be frozen with respect to the thermodynamic ...
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Quenched and annealed disorder in a combinatorial problem

For a research project I'm dealing with a combinatorial problem which I am modeling as a disordered system. For some context, the problem is the TSP, and the disorder enters through the weights on its ...
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2 answers
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Question about molecules and their movement

This question might be nonsensical and, if it is, please leave a reply so I know and can remove it. I'm currently learning about basic thermodynamics and was thinking, if there is some "average&...
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Averaging SYK models and the disappearance of the density matrix

In A strongly correlated metal built from Sachdev-Ye-Kitaev models by Song et al. they wish to calculate the generating function for a system with quenched disorder. In the Keldysh formalism, this ...
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What is the physical meaning of entropy rate?

When I first heard about the notion of "entropy rate", I thought it should be something like a derivative form of entropy. I know what entropy indicates in view of (dis)order. However, after ...
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What does the characteristic temperature T0 in Variable Range Hopping (VRH) mean?

In Variable Range Hopping, the conductivity could be expressed as σ=σ0exp[-(T0/T)p] where T0 is the characteristic temperature. What is its physical meaning?
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What is the precise relation between level compressibility and the spectral form factor?

In the study of disordered conductors, the level number variance is defined as $$\Sigma_2 (\langle n \rangle) \equiv \langle n^2 \rangle-\langle n \rangle^2 ~, $$ where angular brackets denote ...
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Reading materials on Lee-Yang zeroes for spin systems with quenched disorder

I am trying to have a deeper understanding of the Lee-Yang zeros for spin systems with quenched disorder. So far I have read Section 3.2 of Itzykson-Drouffe which covers the concept for Ising model. ...
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1 answer
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References for prerequisite material for understanding papers on Generalized Global Symmetries

I want to understand the papers https://arxiv.org/abs/1412.5148 and https://arxiv.org/abs/1703.00501. Assuming that I understand basics of gauge theories, could someone suggest some references ...
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Derivation of Lyapunov exponent in 1D disordered system

What I am considering is a tight-binding model of 1D disordered system. According to the literature (page 1500, equation (60)), Lyapunov exponent $\gamma$ is calculated as follows which I am not ...
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1 answer
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Weak localization, strong localization, and localization without a metal-insulator transition

As I begin to read literature on Anderson localization by disorder, authors are distinguishing between cases that are unfamiliar to me, namely weak localization, strong localization, and localization ...
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Why is a symmetric traceless tensor zero when averaged over all directions?

In page 168 in Ref. [1], the authors search for a suitable order parameter for the nematic phase in liquid crystal. If $\vec v^\alpha$ is the direction of a single molecule, than due to the inversion ...
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Complete localization in 2D

The two-dimensional Anderson model is the model $$ H = T + \lambda V_\omega $$ where $T$ is nearest-neighbor hopping on $\mathbb{Z}^2$ and $V_\omega$ is a random potential. $\lambda > 0$ is the ...
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Random Fermion Hopping Model

Consider a random, all to all, complex fermion hopping model on $N$ sites with quenched (Gaussian) disorder, that has a well defined large $N$ limit (aka the SYK2 model). So, we start with free ...
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De Almeida-Thouless line and spin glass in the Hopfield network

From the SK model, the Almeida-Thouless line appears to divide the stable paramagnetic phase and unstable spin-glass phase in the presence of an external magnetic field. However, in the case of a ...
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1 answer
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Level statistics of many body localization

I was calculating some Hamiltonian's spectrum statistics. Namely, I calculated the Hamiltonian's eigenvalues and sorted them in an ascending order: $E_1,E_2,E_3...E_N$. The quantity I calculated is r, ...
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What is the intuition behind the statement that non-equilibrium systems with static disorder are self-averaging?

In this paper(1) by C. De Dominics, he makes the argument that in a dynamical statistical mechanics system, one doesn't need to apply the replica trick and can directly disorder average the generating ...
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If universe is expanding shouldn't its 'disorderness' decrease?

I've came across Clausius Inequality which says that entropy of an isolated system always increases (in an irreversible process). Assuming universe to be an isolated system, a time will come when ...
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Calculate an order parameter for a given set of atomic coordinates

I have a box which contains a few thousand atoms, and I would like to be able to calculate a single number which gives some indication of how ordered their arrangement is in 3D. For example, if they ...
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What is(are) the effect(s) of disorder on electrical conductivity?

As a non-specialist, I asked the question "What are disorders in condensed matter parlance?" about the meaning of disorder in condensed matter physics. I also wrote a non-specialist answer after some ...
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What are disorders in condensed matter parlance?

Condensed matter physicists often use the term disorder. What is a disorder? Is it some point defect or line defect? How are they modelled in a theory?
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Why do we disorder-average before/after taking the logarithm of the partition function for annealed/quenched disorder?

Pg. 19 of these notes says Crucially, the [disorder] average $\overline{\log Z}$ has to be computed after taking the logarithm. Such an average is called quenched ... Computing the average first, ...
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Difference between Anderson localization and weak localization

I have read that weak localization is a precursor to Anderson localization. Weak localization happens due to the constructive interference between paths that loop around in opposite direction, on ...
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Derivation of the gradient expansion of the Keldysh nonlinear sigma model for disorder metals

My confusion relates to Appendix C of this this paper although the same derivation is presented in many others. When deriving the gradient expansion of this term arrives at a term quadratic in the ...
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Are maximum order and maximum disorder equally easy to describe?

If we have a collection of particles in a maximum ordered state, is this state just as easy to describe as a collection of particles in a minimum ordered state? If we have a collection of particles ...
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2 votes
3 answers
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What does the second law of thermodynamics really mean?

I started reading about entropy and the second law of thermodynamics. Different sites give different definitions and meanings of this law. A few of them: Disorder always increases heat always flows ...
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2 votes
1 answer
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Fractal structure in colloidal systems

In describing the configuration of a colloidal system, one often deals with either, disordered fluid states, disordered jammed states or crystalline states (so an underlying lattice structure), but in ...
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Quenched systems - disorder average (SYK model)

In a system with quenched disorder one is usually looking for self-averaging quantities, i.e., quantities such that the average over the couplings produces a ``typical" configuration in the ...
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Single-electron propagator in disordered media: higher moments?

The known result that the impurity-averaged single electron propagator takes the form $ \langle G_0(r) \rangle \sim e^{-|r|/\ell} $, for $\ell$ the mean free path is frequently quoted by papers on ...
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Superconductor-insulator transition at finite temperatures

I know that it is possible to have a phase transition at $T=0$ between a superconductor and an insulator. The mechanism is not the "usual" QPT as the system is not translationally invariant: the ...
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Do hydroelectric power plants violate the popular scientific notion of entropy = disorder?

I had a discussion yesterday, and I found my understanding of entropy lacking. I know that entropy is not exactly the same as the degree of disorder in a system, but I also know that outside of ...
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1 vote
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Why does entropy arise from order?

Why does entropy arise from order? Thanks. I'm not sure if this question has already been answered on this site. If anyone needs me to clarify the question, please post in the comments and I'll ...
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4 votes
2 answers
982 views

Difference Between Ruderman-Kittel-Kasuya-Yosida (RKKY) Interaction and Kondo Effect

The question is in the title. I don't understand the difference between these two effects. Based on my understanding, the Kondo Effect is where the conduction electrons effectively screen a local ...
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What is a zero temperature horizon?

While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this: We are interested in solutions with a zero temperature ...
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1 answer
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Conductance of disordered conductor

I'm struggling with a rather advanced problem. Consider a conductor placed between two leads. The conductor is not completely clean but contains all kinds of impurities. The goal is to find the ...
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1 answer
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Physical understanding of Anderson (disorder) localisation

My current understanding is that waves in disordered potentials experience localisation due to interference effects. (eg an electron in a disordered medium tries to take different paths of effectively ...
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1 vote
0 answers
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Why doesn't entropy get decreased in adiabatic expansion process?

I was reading the second step of Carnot cycle in which the system undergoes adiabatic expansion doing work & thus decreasing the internal energy of itself. The entropy didn't change as no further ...
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1 vote
0 answers
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phonon dispersion with random masses

In order to see how phonons should be affected by disorder, I've been playing around with a model involving a 1D chain of masses linked by springs, where the spring strengths are all the same but the ...
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13 votes
2 answers
1k views

scaling theory of Anderson localization

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$ His question was whether the eigenstates ...
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Why does the diffusion pole universally appear in the two-particle Greens function (diffuson)

I've been thinking about the calculation of the diffuson in the context of impurity-averaged Greens functions. If you calculate the two-particle Greens function in the ladder approximation (for ...
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3 votes
2 answers
246 views

Entropy / Structure Relations

I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? The further a system is from its maximum ...
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0 votes
1 answer
201 views

Orienational order parameter in isotropic systems

I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter $S$ is often used: $$ S=\left\langle\frac{1}{2}\left(3\cos^2\theta−1\right)\right\rangle $...
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Maximising entropy when energy is shared between systems

This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble. I don't understand why there should be a minus sign in the middle, if Energy* is ...
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2 votes
2 answers
108 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
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4 votes
1 answer
406 views

Confusions regarding entropy

Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such as an ice/solid has a lower entropy than its gaseous equivalent and that a process such as ...
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1 vote
2 answers
285 views

Qualitative discussion about entropy and disorder

Many discussions about entropy and disorder use examples of decks of cards, pages of books thrown in the air, two gases being mixed in a container, even the state of a nursery at the end of the day ...
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5 votes
2 answers
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Entropy: two explanations for the same quantity?

I studied thermodynamics and I saw the following definition for entropy: $$ \Delta S = \int_1^2 \frac{\text{d}Q}{T} $$ that we use to calculate $\Delta S$ for different types of transformations. In ...
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4 votes
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Qualitative argument to determine energy of defects

In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that: 2D In two dimensions, the mean energy of an isolated point defect in a square ...
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11 votes
1 answer
2k views

Interpretation of the Random Schrödinger Equation

I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper ...
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