Acoustic Signatures of the Phases and Phase Transitions in the Blume Capel Model with Random Crystal Field

<div>Double logarithmic plots of attenuation versus <svg height="12.5794pt" id="M237" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 51.4255 12.5794" width="51.4255pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,12.564,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,23.101,0)"><path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 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low-frequency and (b) high-frequency regimes in the neighborhood of a critical point for <span class="nowrap"><svg height="11.7782pt" id="M238" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 44.5261 11.7782" width="44.5261pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path></g><g transform="matrix(.013,0,0,-0.013,11.342,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g 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Advances in Condensed Matter Physics

fig5

Figure 5

Figure 5: Acoustic Signatures of the Phases and Phase Transitions in the Blume Capel Model with Random Crystal Field 