In this blog post, we will examine the concept of critical phenomena through the Bachhausen effect and learn how it applies to natural and social phenomena.

Critical phenomena and the Bachhausen effect: Dynamic transitions at the boundary between order and disorder

Physical systems undergo a process of transition from one state to another in response to changes in external environmental factors. During this transition process, unusual physical reactions that occur between order and disorder, or between different states of order, are called critical phenomena. This is a very important concept in complex systems science and statistical physics, and is a phenomenon that is universally observed not only in the natural world but also in social systems. One of the most representative examples of critical phenomena is the Barkhausen effect observed in magnetic materials. Various theoretical models have been proposed to understand and explain this phenomenon. The Barkhausen effect was first observed in experiments conducted by German physicist Heinrich Barkhausen in the early 20th century. He inserted a magnet into a wire coil and gradually changed the external magnetic field, measuring the change in the electromotive force induced in the coil.
Generally, according to Faraday’s law of electromagnetic induction, when a magnetic field changes, a change in magnetic flux occurs, which induces a current in the coil. However, in this experiment, even when the external magnetic field was continuously changed, the current induced in the coil appeared as irregular and sudden jumps. This phenomenon, in which the change in magnetic flux is not continuous but occurs in small jumps, is called the Barkhausen effect.

The basis of magnetism: electron spin and magnetic domains

So why does this irregular reaction occur? At the heart of this phenomenon is electron spin. Electron spin is a unique physical quantity defined by quantum mechanics and is a fundamental factor that determines the magnetism of a material.
Strongly magnetic elements such as iron, cobalt, and nickel exhibit magnetic properties because their electron spins are aligned in the same direction. These aligned spins maintain a stable order, and when a strong external magnetic field is applied, the spins realign themselves in the direction of the magnetic field, transitioning to a state of higher order.
If an external magnetic field is applied in the opposite direction, the alignment of the spins also reverses, and they transition to another stable state of order. This process does not occur with individual spins moving independently, but rather with a collective region of spins aligned in the same direction, called a magnetic domain. When a magnetic field of a certain size is applied, these magnetic domains are irregularly rearranged, and the Bachhausen effect occurs.
The external magnetic field at the point at which the Barkhausen effect is observed is called the critical magnetic field, which is the critical point at which the magnetic material breaks its previous order and transitions to a new order.

Characteristics of critical phenomena: irregularity and correlation length

In critical phenomena, the components within a system form irregular clusters and fluctuate. These clustered fluctuations are one of the key characteristics of critical phenomena. As a result, the dynamic properties of such systems are difficult to explain using classical analytical methods and require a statistical physics approach instead.
An important concept in this process is correlation length. Correlation length refers to the range within which individual elements in a system can influence each other, and this distance increases rapidly as the critical point is reached. In the case of the Barkhausen effect, the size of the magnetic domain formed by the interaction between spins corresponds to the correlation length.
An increase in correlation length means that small changes in some spins can affect the entire system beyond the neighboring areas. This makes it impossible to clearly define the range of interactions that govern the system, and eventually, a state without a fixed scale, or scale-free characteristics, appears.
This scale-free property is expressed mathematically as a power law. Recent experiments have confirmed that the distribution of magnetic fluctuations observed in the Barkhausen effect follows a power law. In other words, small fluctuations occur frequently, while large fluctuations occur rarely, but they maintain a specific ratio and constitute the overall distribution.

Power laws and self-organization: a common language for various systems

In addition to the Bachhausen effect, the same power law appears in various physical transitions, such as when magma cools and solidifies into rock, when metals become magnets, and when conductors transition to superconductors. This means that regardless of the type of physical system, universal dynamic characteristics appear when a critical phenomenon occurs.
This universality is very significant to scientists because when various systems change their state of order due to external stimuli, similar patterns are repeated in the transition process. To explain this, the concept of self-organization was introduced. This is a theory that the components within a system spontaneously form order without external manipulation and reach a critical state.
Surprisingly, these power laws are found not only in physical systems but also in social, biological, and information systems. For example, power law distributions are observed in the conflict between buying and selling forces in the stock market, earthquakes caused by the accumulation and release of pressure between tectonic plates, complex interactions between neural networks and cells, and the connection structure of the Internet network.

Conclusion

Critical phenomena and the Bachhausen effect go beyond simple physical observations and provide a key framework for explaining how complex systems evolve between order and disorder. The power law that appears in this process acts as a universal law that can be applied not only to physics but also to various fields such as economics, biology, and social sciences.
Even in phenomena that appear complex and disorderly, we can discover the hidden order of nature through the existence of certain patterns and rules. Critical phenomena are an important key to capturing that order, and their applicability and theoretical expansion are expected to continue in various fields in the future.